
Class 

Book.. 



COPYRIGHT DEPOSE 



Essentials of Logic 



I^[l!ll 



Essentials of Logic 



By 

William Dinwiddie, LL.D, 

Chancellor, and Professor of Philosophy, 
Southwestern Presbyterian University 




New York 

The Neale Publishing Company 

1914 






Copyright, 1914, by 
The Neale Publishing Company 



MAY -5 1914 



CI.A369956 



CONTENTS 

PART I 

GENERAL 
CHAPTER PAGE 

I What Logic Is n 

II Notions 15 

III The Primary Laws of Thought . . 46 

IV Propositions 52 

PART II 

DEDUCTIVE INFERENCE 

V Immediate Deduction 75 

VI Mediate Deduction 86 

VII Deductive Fallacies 122 

PART III 

INDUCTIVE INFERENCE 

VIII The Nature and Laws of Induction . 139 
IX The Causal Basis for Induction . . 146 

X Results of Induction 169 

Index 175 



PREFACE 

This is intended to be a working handbook of 
logic, and not a history of the subject. No nov- 
elty is claimed, except the novelty of simplicity, and 
freedom from needless technicalities, hereditary 
nomenclature, and other barnacles ; as, for example, 
in the treatment of the syllogism and of fallacies. 
With teachableness and early practical application 
in view, traditional accretions and controversies 
have been omitted; and yet, it is believed, without 
sacrifice of essentials. There is constant endeavor 
to make evident the relation between different parts 
of the subject. 

Quotation marks have been used freely where 
they seemed advantageous, but not according to any 
hard and fast rule. 

The book contains a large collection of examples 
for practice, selected also for their intrinsic value, 
and illustrating the forms of thought that occur in 
actual literature, and not merely in logical exer- 
cises. Adequate use of these will double the work- 
ing length of the book. 

W. D. 

Clarksville, Tennessee, 
October, 1913. 



PART I — GENERAL 



ESSENTIALS OF LOGIC 

CHAPTER I 

WHAT LOGIC IS 

i. Logic Defined. — Correctness of thought is 
vital to success in everyday affairs, to progress in 
knowledge, to science, to literature, to philosophy, 
to theology, to logic itself. Hence it is of great 
importance to know the laws of correct thinking, 
and this knowledge is acquired by the study of 
logic, which may be defined as the science of the 
forms and laws of correct thought. 

2. Logic not Art but Science. — Science dif- 
fers from other knowledge in being systematically 
arranged. Science is knowledge classified or sys- 
tematized. Such knowledge often forms the basis 
for the highest skill, or art; but art is concerned 
with doing, science with knowing. The closeness 
of this relation of science and art is the reason why 
the two are often confused or identified. A man, 
however, may know the science of architecture in 
minute detail, and yet not have the art to build; a 
doctor may know the position and use of every tis- 
sue in the body, and yet have no skill as a surgeon. 

ii 



12 ESSENTIALS OF LOGIC 

Logic is a science, not an art. Logic does not 
give us the power to think correctly, but it acquaints 
us with the laws of correct thought; it gives us the 
knowledge of what correct thinking must be. The 
ability to think correctly may be possessed without 
the study of formal logic, for it is an ability natural 
to man, but fuller knowledge of What is correct in 
thought results naturally and increasingly in the 
use of what is correct. 

3. Logic a Distinct Science. — Scientific 
knowledge is divided into* branches, each called a 
science, and each distinguished from others by the 
distinct nature of the facts it investigates and sys- 
tematizes. Systematized facts as to the human body 
form the sciences of anatomy and physiology; the 
plants give us botany; the stars, astronomy; the 
weather, meteorology; the mind, psychology; 
thought gives logic. The distinctness of logic from 
other sciences is due to the distinctness of the facts 
of thought from the facts treated of in other sci- 
ences. 

We need to distinguish carefully from each other 
sciences whose facts are closely related, as physiol- 
ogy and anatomy, physics and chemistry, geology 
and mineralogy, psychology and logic, or grammar 
and logic. Grammar, psychology, and logic all have 
to do with thought. Grammar, however, is con- 
cerned not with the correctness of the thought, but 
merely with the expression of the thought; that is, 



WHAT LOGIC IS 13 

with the language. Psychology treats of thought 
solely as an activity of mind, while logic deals with 
the thought itself; psychology looks at the mind as 
it thinks, logic at the thought ; psychology considers 
the mind as it produces thoughts, logic considers the 
product. Psychology asks: What does the mind 
do when it thinks? Logic asks: What is the 
thought ? 

As to the nature of thought it is enough to say 
here, somewhat loosely, that the affirmation or the 
denial that one of two things, groups of things, 
qualities, or ideas is related to the other of the two, 
is a product of thought, or, in brief, a thought. 
For such affirmation or denial to be warranted, it 
is evident that its two terms, the subject and the 
predicate, must first have been compared in mind 
with each other or with some third term. Thought 
affirms or denies that one thing is contained in or 
comprised under another. 

4. Logic Related to All Science. — Since sci- 
ence is knowledge classified or systematized, and 
since it is thought that classifies or systematizes, and 
logic that treats of thought, it follows that logic is 
vitally related to every science. The things we 
think about are many; the correct ways we think 
about them are few; and as everything we think 
about must be thought about in some definite way, 
or form, according to some definite law, if we think 
correctly ; then it follows that the science of any set 



14 ESSENTIALS OF LOGIC 

of things or facts depends on the forms or laws 
correct thought must use, in other words, on the 
facts of logic. Since all science involves thought, 
every science depends on logic, the science of 
thought. Logic itself can be a science only by con- 
forming to the laws of thought of which logic 
treats. 

Logic, then, is a science of forms in which a 
countless variety of thoughts about many things 
may be cast. Logic treats, not of the things we 
think about, but of the ways in which we think 
about things, in trivial everyday affairs or in high- 
est regions of scientific deliberation. Its realm is 
the universe of thought. One of the forms of 
thought is the term, or notion. Examples of the 
notion are: apple, red, sphere, thought, man, each 
of which, as will appear later, stands for the result 
of prior comparisons. Other thought-forms are 
judgments, by means of which we affirm or deny 
that two notions are related to each other, as : the 
earth is a sphere, snow is white, justice is not 
mercy; also, subject and predicate, genera and spe- 
cies, inferences, syllogisms, and many others. The 
form can be made clear only by filling it with mat- 
ter, which is a step beyond pure logic, but used 
freely in pure logic for illustration. 



CHAPTER II 

NOTIONS 

5. What Notions Are. — Grammatically, a no- 
tion is a noun or an adjective, as for example, " ap- 
ple," " red " ; logically, a notion is either a " mark," 
or quality of a thing, as red is a quality of apple; 
or the notion stands for a group of qualities, and is 
called a concept, as apple stands for round, juicy, 
edible, etc. ; or it stands for a group of things, as 
apple stands for every member of the group called 
by that name; psychologically, the notion is the re- 
sult of abstraction, conception, and generalization. 
For example, looking at a certain object, we " ab- 
stract," or take away in our minds, and consider 
apart from other qualities, that which we see, and 
say, the object is red ; handling it, we abstract shape 
and weight from other qualities and say, it is round, 
it is heavy; smelling it, we say it is fragrant, and 
so for each quality perceived by the senses. It is 
evident that abstraction is purely a mental process 
in no way affecting the object or its qualities. Each 
of the abstractions above is expressed in the form of 
a " judgment," which is thus used in forming no- 

iS 



16 ESSENTIALS OF LOGIC 

tions, as well as the notion in forming other judg- 
ments. The judgment is discussed in Chapter IV. 

The second mental step in forming a notion gath- 
ers into one the various marks noted by abstraction, 
and for convenience gives this bundle of marks a 
name. This bundle of marks is called " concept," 
or " gathered together." Thus the red, round, 
heavy, juicy, edible object of the above illustration 
of abstraction is called " apple " ; and apple is the 
concept which includes, or " connotes " the marks 
red, round, etc. 

The third mental step in forming a notion is gen- 
eralization. The marks red, etc., and the concept 
apple refer only to the one particular object we have 
been examining; but we receive similar impressions 
from other objects, and we say they are red, round, 
juicy, etc. ; that is, all these objects have these 
marks, all are apples. Thus we " generalize " the 
concept apple, we say it includes every object of a 
certain group, or class, or " genus." In this way 
we classify our knowledge, we get the genera of 
science. 

The order in which conception and generaliza- 
tion are mentioned above is arbitrary. We may 
either bundle the marks of one object into a con- 
cept and then generalize, or we may observe a num- 
ber of objects having similar marks, and generalize 
each of these marks before forming them into a 
concept. 



NOTIONS 17 

Marks and concepts are notions. Each form can 
be changed into the other. The difference is solely 
in the way the form is used, and may be disregarded 
in the development of the science of logic. 

It is evident that a concept may be viewed as a 
group of marks or a group of things. " Apple" is 
said to " connote " the marks juicy, subacid, etc., 
and to " denote " all apples. To give the marks 
which a notion includes is to " define " it; to give 
the classes of things contained under a notion is to 
" divide " it. Logical definition and division are 
discussed in sections 7 b and 7 c below. 

Many concepts include a practically unlimited 
number of marks : hence in defining the concept by 
giving its marks, we select only those essential to 
the nature of the object or the class, those without 
which the object would not be what it is. The con- 
cept man includes the marks, two-legged, having 
hair on the head, erect, and many others, the absence 
of which would still allow the objects denoted by 
the concept to be men; but the marks animal and 
rational must be present, else the objects denoted 
will not be men. 

According to what is known as " the law of in- 
verse ratio," the fewer marks a concept contains, 
the greater the number of things it includes, and 
the reverse. If to the marks of apple we add 
" red," the objects included under " red apple " are 
evidently fewer than those under " apple " ; if from 



18 ESSENTIALS OF LOGIC 

the marks of " rocking-chair " we take the mark 
" rocking," we have " chair," a class containing 
more objects than " rocking-chair." All the marks 
contained in a concept are called the " intension " of 
the concept; the things contained under a concept 
are called the " extension " of the concept; and the 
above law of inverse ratio may be stated thus : The 
greater the intension, the less the extension, and the 
reverse. 

A notion is also called a " term " (Latin, 
terminus, end), because in its use as subject or predi- 
cate it is the end of the sentence. A notion often 
consists of a group of words, as, for example: 
North American Indians, rivers which flow into the 
Atlantic Ocean. 

PRACTICE ON SECTION 5 

1. What marks do you find in your notion of gov- 

ernment, campus, home, railroad, beauty, food, 
athletics, miser, education, money? 

2. What classes or kinds do you think of as included 

under each of the above notions? 

3. Name some marks common to two or more of 
these notions. 

4. Name two or more concepts having one of the 

following marks in common: free, heavy, four- 
legged, juicy, upright, smooth, false, yellow. 

5. Does every mark you think of as belonging to 
one of these concepts, belong to every one of 
the classes under the concept? 



NOTIONS 19 

6. Can you name a mark that belongs to some of the 
classes under a concept, and not to others? 

7. Add some mark to one of the above concepts, 
and show that the resulting concept denotes fewer 
things; then add other marks successively, not- 
ing the effect on the number of things. 

8. Illustrate any of the above exercises by using 
five other concepts. 

9. Add two classes of things, such as acute and right 

triangle, say what mark has been lost, then add 
another class to the result, and so on. 

10. Give other illustrations of the above exercise. 

11. Illustrate abstraction, conception, and generaliza- 
tion by any of the above notions. 

12. State the intension and the extension of any of 
the above notions. 

13. Change any of them from marks to concepts, and 
the reverse. 

14. Name some of the marks connoted and some of 
the kinds denoted by each of the two meanings 
of the following terms: school, band, mark, no- 
tion, bed, log, yard, party. 

15. Would a perfect language have words of two 
meanings ? 

6. Kinds of Notions. — The following are the 
most important of the many ways in which notions 
may be grouped in classes: 

6 a. Notions are " concrete " or " abstract." 
A concrete notion is the name of a thing or of a 
quality thought as being in a thing: for example, 



20 ESSENTIALS OF LOGIC 

" green " is a concrete notion, because it can in this 
form be thought only as belonging to grass or other 
green things. It is of course the adjective and not 
the noun " green," of which this is true. An ab- 
stract notion is a quality of a thing thought as being 
itself a separate thing; for example, greenness, 
truth, morality, hardness. These are not things, 
though named as if they were; they are qualities 
only; respectively, say, of grass, assertions, conduct, 
iron. All adjectives are concrete. Many nouns 
originally abstract have by change in usage become 
concrete; as, "relation" for "relative," "action" 
for " act." 

6 b. Notions are " particular " or " general." 
A particular, or " singular," or " individual " no- 
tion denotes one object; as John, Mr. Brown, this 
hat, my house. The objects we see, hear, or know 
through any sense, are particular objects. Abstrac- 
tion and conception, the first two steps in the forma- 
tion of notions, described in Section 5, have to do 
with particular notions; the third step, generaliza- 
tion, with the general notion, or the notion which 
denotes a " genus," or " kind," or " class " ; as 
martyr, bean, horse, and all common nouns. The 
general does not exist except in thought ; real things 
are individual, singular, particular, and not general. 
The general notion, however, is often made to de- 
note a particular object by the use of some limiting 
word or group of words, as " this," " that," " his," 



NOTIONS 21 

" the," a relative clause, etc. Sometimes there is 
ambiguity, and care must be taken, as always, to get 
at the actual meaning of the words. For example, 
in the sentence: a man is a complex creature, "a 
man " is general, and the meaning is the same as : 
man is a complex creature; but in the sentence: a 
man is running down the street, " a man " is partic- 
ular, denoting only one man. Again, in: the ox is 
patient, and, the ox is dead, we have the double use 
of " the " ; the first either general or particular, the 
second particular. The limiting words, phrases, or 
clauses, which thus reduce the general notion to 
the particular, are called " particular marks." 

It is therefore obvious that all strictly proper 
names are particular. The difference between the 
proper name and the common name in its particular 
use, as above, is that the latter implies marks, the 
former not. For example, " George " has no mean- 
ing whatever, is a mere sign arbitrarily associated 
with an individual person ; but to designate the same 
person George as " that boy," attributes to him all 
the marks of the concept " boy." So-called proper 
names, however, often show sex, or other marks, 
and are to that extent not strictly proper: John is 
of the male sex; the latter part of " Clarksville " 
means city; so "port," "burg," "ton," and other 
parts of names. 

A proper noun may be used as a general name, 
some prominent mark possessed by the owner of 



22 ESSENTIALS OF LOGIC 

a well-known proper name being thus attributed to 
others; as, a Daniel come to judgment; or, he is a 
Nero, a Herod. 

6 c. Notions are " obscure " or " clear." 
Obscure notions are those not well enough known 
to be separated in thought from others nearly alike ; 
as, perhaps, caribou, moose; adhesion, cohesion, at- 
traction; college, university; thought, feeling, con- 
sciousness, desire; memory, imagination. On the 
other hand, we have a clear knowledge of dog, 
house, ocean, school, etc. 

Clear notions may be " indistinct " or " distinct." 
We have a clear notion of " grass " for example, 
but our knowledge is not distinct unless we know 
the marks and the kinds of grass. " Table," " car- 
pet," " bread," " book " are examples of notions 
distinctly known, for we know their marks and 
their kinds, the two phases or parts of distinct 
knowledge. 

It appears that clearness is attained by denials, 
which say what a thing is not; distinctness by af- 
firmations, which say what a thing is : as, he is no 
fool, he is a man of great ability; a mandolin is 
not a violin, it is not played with a bow, it has a 
larger air-chamber, it is played with a plectrum. 

Distinct notions may be " inadequate " or " ade- 
quate." Inadequate notions are those that do not 
imply enough marks for them to represent accurately 
and fully the things in question; while adequate 



NOTIONS 23 

notions are those which imply enough marks for the 
particular purpose in view. 

Distinct notions are also " intuitive " or " sym- 
bolic." Intuitive notions are those used in thought 
by means of a mental image of one of the things 
included under the notion; as, for example, bed, 
house, dog, if accompanied by a visual image of a 
bed, a house, a dog ; or intuitive notions may be ac- 
companied by the actual perception of one object 
of the class, as when we are looking at a bed, etc., 
or at a picture of the object. If not so accom- 
panied, the words, bed, house, dog, etc., are mere 
symbols, and we do not look the thing in the face, 
as " intuition " means. Many notions, therefore, 
may be used either intuitively or symbolically ; many 
others are too complex to be imaged by the mind, 
and can be used only symbolically; as, education, 
prosperity, peace, the velocity of light, the govern- 
ment of the United States. 

Perfect knowledge is clear, distinct, adequate, 
intuitive. Most of our knowledge is imperfect ; but 
the possibility of progress toward perfection is ever- 
present, and the effort to make the progress is a 
duty. 

Language is the vehicle and the storehouse of 
thought, and the notion is the fundamental word. 
The child can make its wants known surprisingly 
well without other words than the noun. A verb 
can be resolved always into the verb " be " and a 



24 ESSENTIALS OF LOGIC 

notion. The explanation of the notion is the ex- 
planation of language. Without language, the 
progress of thought would be very narrowly re- 
stricted. By imperfect language, the accuracy and 
the communication of thought are jeopardized. 
The abstract should be frequently tested by the con- 
crete, the general by the particular, the symbolic by 
the intuitive. 

6 d. The following classifications of marks 
are important: 

ist. Marks are " positive," or " negative " : 
" wet " is a positive, " dry " a negative mark, mean- 
ing merely the absence of moisture. Marks are 
positive or negative in themselves, without regard 
to any particular concept to which they may be- 
long. 

2nd. Marks are " essential " or " accidental " ; 
as, " for heating " is an essential, " self-feeding " 
an accidental mark of stove. Marks are not essen- 
tial or accidental in themselves, but with regard to 
the concepts to which they belong. 

3rd. Marks are " common " or " peculiar," ac- 
cording as they belong to a concept in common with 
other concepts, or belong to that concept only : " liv- 
ing " is common to man and horse, " laughing " is 
peculiar to man, " neighing " is peculiar to horse. 



NOTIONS 25 

PRACTICE ON SECTION 6 

1. Name ten concrete, and ten abstract notions. 

2. Name five concrete, and the five corresponding 

abstract terms. 

3. Change the following notions from general to 
particular, or the reverse: bread, a storm, the 
horse, truth, pleasure, fire, charity, king, that 
tree. 

4. Which, if any, of the following are proper names : 

Caesar, Czar, Kaiser, Pharaoh, President, Mr. 
President, Bible, Episcopal Prayer-Book, High 
School, University of Berlin, Mathematics? 
What marks are connoted by any which are not 
proper names? 

5. Write a list of ten general terms. Of ten par- 
ticular terms. 

6. Mention several notions not clear to you, naming 
those not separated clearly from them in your 
thought. 

7. What are some notions you know clearly, but not 

distinctly ? 

8. Can you think of a notion you know clearly and 

distinctly, but not adequately? 

9. Give examples of the intuitive and the symbolic 
representation of several concepts. 

10. Mention something your knowledge of which you 

deem perfect. 

11. Are the following marks positive or negative; 
that is, do they indicate the presence of a quality, 
or mere absence: original, negative, essential, 



26 ESSENTIALS OF LOGIC 

complex, sober, protestant, pure, reckless, rest- 
ful, clean, insane, impartial, silent, dark, weak, 
hard, soft, paralyzed, oblique? 

12. Give the opposite negative or positive mark cor- 

responding to each of the above. 

13. Which of the marks in list a are essential to any 
of the concepts in list b? a. round, juicy, living, 
dead, harmful, peaceable, long-winded, intelligent. 
b. horse, poison, pencil, orange, bore, corpse, 
earth, circle. 

14. Can you name essential marks of house, kitchen, 

stove, study, book, star, plow, spoon, chair, ball, 
bird, dog, logic, college? 

15. Name, if you can, notions of which one of the 
following is an essential mark : square, blue, loud, 
sour, smooth, fragrant, animal, logical, mental, 
conscious, extended, rational, military, strong, 
scientific, stingy. 

16. Use 14 and 15 above, substituting accidental for 

essential. 

17. What marks can you think of that are peculiar 

to any of the notions in 14? What that are 
common to any two or more of these notions? 

7. Relations of Notions. — It was seen in Sec- 
tion 5 that a notion may be viewed either as a group 
of marks or as a class of things, the marks being 
the " intension," the things the " extension " of the 
notion. Intensively, notions may agree, and there- 
fore unite in thought; as, good and great, tall and 
manly, hardness and weight; or they may disagree 



NOTIONS 27 

in the sense that they do not actually co-exist in 
one object, which is however a question of matter, 
not of form, and therefore not in the realm of pure 
logic; for example, a blue toothache, a happy tree; 
or again, the two notions may contradict each other, 
and therefore can not be combined either in thought 
or in fact, which is the only true logical disagree- 
ment; as, theistic and atheistic, wet and dry, 
learned and ignorant. 

Extensively, two notions may represent classes of 
things in any of five relations: 

1st. The two classes may exclude each other 
and not be immediately contained under some wider 
class : as desk and walk, spoon and wheelbarrow. 
This relation may be called " exclusion," and is 
shown by the fact that no member of either class is 
a member of the other. 

2nd. The two notions may exclude each other, 
and yet be immediately contained under some wider 
class; as, Catholic and Protestant under Christian, 
Greek and Roman under Catholic, right angle and 
oblique angle under angle. This is the relation of 
" co-ordination," each notion being of the same rank 
(Latin, ordo) with respect to the wider class imme- 
diately containing it. 

3rd. The relation of the notion contained under 
another to this other is " subordination." 

4th. Again, each of two notions may have a 
part in common with the other, and a part not in 



28 ESSENTIALS OF LOGIC 

common ; as, Europeans and Turks, wholesome food 
and flesh, men and students. This relation is " in- 
tersection." 

5th. Lastly, two notions may be equivalent; as 
negro and darkey, sun and fixed star, leaves and 
foliage. Such notions are said to be in the relation 
of " co-extension." The test is that every member 
of either class is also a member of the other. 

Each notion may be represented by a circle, two 
circles outside of each other illustrating co-ordina- 
tion, if they are contained in a third circle, or ex- 
clusion if there be no third circle; one circle within 
another illustrates subordination; and two inter- 
secting circles, intersection. 

7. a. Classification. — It is evident that a no- 
tion which is subordinate to another may have other 
notions subordinate to it; and that the notion to 
which others are subordinate may itself be sub- 
ordinate to some wider notion, so that a system of 
notions, or classes may be formed. This is classifi- 
cation. 

If, as in co-ordination, two classes exclude each 
other, one of the classes must have at least one mark 
that the other does not have ; or, to state the matter 
differently, one class has a positive mark not be- 
longing to the other, while the other has the cor- 
responding negative mark; without this difference 
in marks, the two classes would of course coincide, 
and the relation would be co-extension instead of co- 



NOTIONS 29 

ordination. For example, Protestant includes the 
mark, denying authority of the Pope, while Catholic 
does not ; right angle has the mark, having a definite 
magnitude, while oblique angle has not. In fact, 
each of two co-ordinate classes contains every mark 
of the wider class to which they are subordinate, 
and each contains in addition one other mark; as, 
Catholic and Protestant contain all the marks of 
Christian, and in addition, respectively, the marks, 
accepting the authority of the Pope, and, not accept- 
ing the authority of the Pope; or, the classes red 
raspberries and raspberries of other colors have each 
all the marks of the class raspberry, and in addi- 
tion, respectively, the marks red and not-red. 

It is evident that we are here considering the 
three processes in the formation of concepts, de- 
scribed in Section 5, from a somewhat different 
point of view ; for it is by abstraction that we learn 
the marks, by conception that we form the notion, 
and when we generalize, we form a class. It is 
further evident that the law of inverse ratio, of Sec- 
tion 5, applies here, so that each of two co-ordinate 
classes, as man and brute, having each one mark, 
as rational and non-rational, respectively, more than 
the wider class, animal, to which they belong, con- 
tains fewer things. To add marks is to diminish 
the number of things included under the concept, to 
divide the things under the former concept into two 
classes, one having the mark in question, the other 



So ESSENTIALS OF LOGIC 

not; it is to classify, to make classes, or species. 
On the other hand, to take away marks is to add 
things, to generalize, to make genera (plural of 
genus). So genus and species are relative terms; 
any genus may be divided into species, and these 
species may in turn be genera of lower species; so 
any genus except the highest may be in turn a spe- 
cies under a higher genus. 

What are the limits to the process? How far 
can we continue to add marks, to cut off things? 
Theoretically, until all common marks are included, 
that is, until we reach a class such that not even 
any two of its members have a common mark which 
is not also a mark of all the other members of the 
class. In such a case there can be no further di- 
vision into classes, for unless at least two things 
have such a common mark, division will result not 
in classes or species, but in separate individuals; 
and if all the other members of the class have the 
only marks that are common to any members, any 
attempt at division would include the whole class, 
and be no division. For example, a group of men 
contains one lawyer, one doctor, one merchant, one 
statesman, and one railroad president, and can be 
divided on the basis of profession only into indi- 
viduals. This illustrates the lowest logical species, 
the species that can not be a genus and be divided 
into lower species, but only into individuals. 

On the other hand, how far can we continue to 



NOTIONS 31 

generalize, to subtract marks, to add things ? Theo- 
retically, until all things are included. Disregard- 
ing the metaphysical distinction of matter and form, 
the widest class, the " summum genus," therefore, 
is " thing," which has only the one mark, " exist- 
ing," and denotes everything. For practical sci- 
entific ends, classifications do not have to begin with 
this highest class, but with the class most suitable in 
the different sciences. Astronomy, for example, 
starts with heavenly body ; botany, with plant ; and so 
on. When we do not know the proper class for an 
object, or do not care to be scientific, we refer it to 
the " summum genus," and call it a " thing." 

The two relations of notions, co-ordination and 
intersection, are of such importance that they are 
treated more in detail in Sections 7 b and 7 c imme- 
diately below. 

PRACTICE ON SECTIONS 7 and 7 a 

1. Pick from the following such pairs of notions as 

(1) may unite in thought, or (2) do not actually 
unite in an object, or (3) can not unite in thought 
or in fact: wide, clear, poor, savage, blue, sweet, 
arm, pain, wealthy, mean, man, music, sorrow, 
gentle, short. 

2. Illustrate the five extensive relations by various 
pairs of notions. 

3. Draw a pair of circles representing each of these 

relations. 

4. Show that the following notions are subordi- 



32 ESSENTIALS OF LOGIC 

nate to other notions, and also have other notions 
subordinate to them: lock, brick, grass, dog, con- 
cept, college, lake, bird, stone, monarchy. 

5. What mark has one member of each of the fol- 

lowing pairs of co-ordinate notions, that the other 
has not? man and brute, straight chair and 
rocker, right triangle and oblique, plant and ani- 
mal, steamer and sailboat (or other kind) ? 

6. What wider class, in each case, includes the pairs 

above, and what mark, positive or negative, has 
each member of the pair, that the wider class 
has not? 

7. Select five other pairs of co-ordinate species, and 
their proximate genera, stating in each case the 
distinctive mark of each species. 

8. See how far you can continue the division into 
species, begun above. 

9. How far can you carry the process in the other 

direction, toward the widest genus? 
10. Can you supply the other species for each upward 

step in 9? 
n. Can you reach a class in 8 or 9 above, beyond 

which the process can not possibly be carried? 

If so, can you say why? 

7. b. Co-ordination and Logical Division. — 

Physical division separates from each other in 
space, actual things or parts of things, as when an 
apple is plucked from the tree, or is cut in two. 
Logical division separates in thought one logical 
class from another. Physical division is " quanti- 



NOTIONS 33 

tative," one amount, part, or quantity being thereby 
separated from another; logical division is "quali- 
tative," for thereby one class having a certain qual- 
ity is thought as separated by the possession of that 
quality from another not having the quality. Phys- 
ically, " a tree " may be divided into any number 
of actual parts, trunk, branches, twigs, leaves, bark, 
roots, etc. ; logically, " tree " may be divided into 
the classes fruit-tree, and other kinds, separated in 
thought from each other by the presence and the 
absence of the mark, fruit-bearing; and in an in- 
definite number of ways by selecting other marks. 
Physically, we divide with a knife; logically, with 
a mark. 

With physical division logic has nothing to do, 
except as a test to distinguish the individual from the 
class; for the individual is pictured in imagination 
as physically divided into parts, and never logically 
into classes, while the general notion or class-name 
is logically divided into classes, and not into parts. 
We may think a notion, however, either " math- 
ematically," that is, as a quantity or an individual, 
separable into parts ; or we may think it " logically," 
as a class, separable into kinds. With reference to 
this mathematical or logical division, notions are 
called " wholes." " A tree " is a mathematical 
whole, for it can not be thought as divided into 
classes ; while " tree " is a logical whole, for it can 
not be divided into parts, but into kinds, as oak-tree, 



34 ESSENTIALS OF LOGIC 

pine-tree, etc. The test for the kind of " whole," 
therefore, is that wholes separable into kinds like 
the whole, are logical ; those separable only into parts 
of the whole, unlike it, are mathematical. 

The division illustrated in Section 7 a, resulting 
in only two co-ordinate classes, differing only in that 
one class has a certain mark, and the other has it 
not, is called "dichotomy" (cut in two). This 
is the only strict logical division, giving contradic- 
tories, as " stone " and " non-stone," " man " and 
" non-man," or under the class, animal, " man and 
brute." "Trichotomy" (cut in three), and " po- 
lytomy " (cut in many) are used for divisions 
other than strictly logical ; as if " tree " be divided 
into oaks, pines, birches, etc. Dichotomy would 
divide tree into oaks and non-oaks, etc. A trichot- 
omy, or a polytomy may be a convenient summary 
of successive dichotomies ; as living things are plants, 
men, and brutes. Apparent continuity in the thing 
divided, or lack of sharp definition of terms often 
makes it difficult to dichotomize, and not leave a 
middle, neutral term ; as in hot and cold, with warm 
between; poor and rich, light and dark. 

Successive logical division, resulting in a logical 
system of classes, must conform to certain rules: 

1st. The same ground of division must be used 
throughout. If not, the resulting classes will over- 
lap, and cause confusion; as if books be divided 
into octavo, duodecimo, works of reference, text- 



NOTIONS 35 

books, Greek, and Latin books. This is called 
" cross division," and the relation between the over- 
lapping classes is not that of co-ordination, but of 
intersection. In the above example, the ground of 
division is first size, then purpose, then language. 

2nd. The one ground of division should be 
an essential (Section 6 d) mark, or a mark 
important for the purpose of the division. The 
ground of division may thus vary according to the 
end in view, but it must not be changed in any one 
system. We might, for instance, divide books ac- 
cording to size to fit our shelves, or according to 
use for convenience of reference, or according to 
language for a similar reason. The scientist for 
varying reasons divides man into classes according 
to race, color, language, religion, government, etc. 

3rd. The genus must be divided into species im- 
mediately subordinate to it. Intermediate classes 
must not be omitted. When geometry is called the 
science of space, science is thought as divided into 
the science of space and other sciences, and an in- 
tervening class, mathematics, is omitted. Science 
should be divided into mathematics and other sci- 
ences, and mathematics into geometry and other 
branches. Such strictness is necessary for scientific 
accuracy, but not for much of the ordinary inter- 
change of thought. We speak of a dog as an af- 
fectionate animal, rather than an affectionate brute, 
thus passing over some of the intervening classes; 



36 ESSENTIALS OF LOGIC 

and of clover as a valuable plant, omitting several 
intervening botanical classes. 

4th. The two classes, or species, resulting from 
division, must constitute the whole of the genus di- 
vided. There must be no part not included, for 
this part would form a third class, and the division 
would not be a dichotomy. If fence be divided 
into rail fence and wire fence, this rule is violated, 
for plank fence, stone fence, etc., are not included. 

PRACTICE ON SECTION 7 b 

1. Indicate the physical, the logical, and the mathe- 
matical division of the following: sword, house, 
dog, grain, school, landscape. 

2. As given, are the above logical or mathematical 

wholes? Transfer each to the other kind of 
whole. 

3. Illustrate the above exercises by five other ex- 
amples. 

4. Divide the following, each in several ways by (1) 

dichotomy; (2) trichotomy; (3) polytomy: 
school, hair, shoe, farm, prison. 

5. Give other examples of these three kinds of divi- 
sion. 

6. State what mark is the basis of the division in 
each example in 4 and 5. 

7. Divide and subdivide any class notion four or 
five times in accordance with Rule I. 

8. Illustrate cross division. 

q. In how many ways can you divide building, for 



NOTIONS 37 

example, and for what important purpose in each 
case? 
10. Test the following for violation of the principles 
of logical division: 

(i) Science: of form and of matter; or, sys- 
tematized and unsystematized. 

(2) Government: monarchy, aristocracy, and 
democracy. 

(3) Flower: annual and perennial; or, shrubs 
and vines. 

(4) Church : Catholic and Protestant ; or, true 
and false. 

(5) Men: moral and immoral; civilized and 
pagan; black and white; laborer and 
capitalist; rich and poor; handsome and 
ugly; native and foreign. 

(6) Thing: animate, inanimate, plant, animal, 
brute, man. 

(7) Student: studious and idle; athletic and 
weak. 

(8) Figure : plane and solid ; rectilinear and 
curvilinear. 

(9) Metal : heavy and light ; precious and 
plentiful ; white and yellow. 

(10) Year: spring, autumn, summer, winter; 
B. C. and A. D. 

(11) The ten virgins : five wise and five foolish. 

(12) Heavenly bodies: planets, meteors, com- 
ets, stars, and suns. 

(13) Brute: animal and other; living and 
dead; biped and quadruped. 



3$ ESSENTIALS OF LOGIC 

(14) Literature: prose, poetry, fiction, drama, 
history. 

(15) Racehorses and carriage horses; automo- 
biles and street-cars. 

(16) His conduct is either foolish or crazy. 

11. Divide and subdivide man so as to include white, 
black, yellow, red; and citizens, to include na- 
tives, Europeans, Germans, Tennesseeans. 

12. Criticise the table of contents of this text on 
logic. 

13. Give examples of violations of Rule 3. 

7. c. Intersection and Logical Definition. — 

Taking the genus man, and selecting the mark, be- 
lieving in a God, we divide man into two species, 
theist, having the chosen mark, and atheist, not hav- 
ing it, thus determining by strict dichotomy two 
classes, theist and atheist, co-ordinate with each 
other and subordinate to the genus, man. We are 
here dealing with the things denoted by the notion 
man, that is, with its extension (Section 5, end), 
and we are looking down the logical scale from 
greater extension to less. 

Again, taking the species, theist, and looking up 
the logical scale, we say, a theist is a man believing 
in a God, or similarly, an atheist is a man not be- 
lieving in a God. This, the reverse of logical di- 
vision, is logical definition, involving a species, its 
proximate genus, and the distinctive mark separat- 
ing the species from its co-ordinate species. This 



NOTIONS 39 

mark is called the " specific difference," that is, the 
mark in which the two species differ. 

The logical relation of intersection (Section 7, 
4th) is here shown; theist, for example, being the 
part common to the two intersecting classes, man, 
and believer in God, each of these two classes hav- 
ing also a part not common to the other. In a 
definition, therefore, the genus and the specific dif- 
ference may be viewed as intersecting notions, the 
notion defined being the common part. 

Here, as always, extensive and intensive forms 
are interchangeable. We may define a theist as a 
human believer in God, thus exchanging genus and 
specific difference; or we may use marks only and 
say, a theist is human and believing in God. This 
purely intensive form is the primary form of the 
definition, which renders a notion distinct by analyz- 
ing it into its component marks, while division ren- 
ders it clear by separating it into classes. 

Logical definition, therefore, requires two essen- 
tial marks (Section 6 a) ; or a genus higher than 
the notion defined and a specific difference; or two 
intersecting classes with a part common and a part 
not common; all these, as we have seen, being es- 
sentially the same. A notion, therefore, having 
only one mark, as, thing, can not be defined. Other 
examples are space, time, infinity, choice. 

An individual can be identified, but not defined, 
for we can not sum up in one all the marks of an 



4 o ESSENTIALS OF LOGIC 

individual save one distinctive mark. There are 
no two intersecting classes whose sole common part 
is an individual. Only general notions may be de- 
fined; individuals may be pointed out, described, 
located in space and time, but not in a logical sys- 
tem. 

A logical definition must be: 

ist. Not too wide. The genus and species, as 
in division, must be proximate, no intervening class 
being omitted. If geometry be defined as the sci- 
ence of space, instead of the mathematics of space, 
this fault is committed. 

2nd. Not too narrow. The specific difference, 
as in division, must be a mark belonging to every 
member of the species, and not only to some, as 
when a dog is defined as an animal that barks, which 
is not true of Eskimo dogs. 

3rd. Not tautological. Neither the name of the 
thing defined nor a synonym or a word of the same 
derivation may be used in the definition, as w T hen 
logic is defined as the science of logical forms, or 
life as the sum of the vital functions. Some of 
the definitions in dictionaries are logical definitions, 
many are mere verbal explanations, by means of 
synonymous terms, and often tautological. This, 
however, may accomplish the purpose of the dic- 
tionary. 

4th. Not superfluous. If a hexagon be defined 
as a polygon with six sides and six angles, this 



NOTIONS 41 

principle is violated; or if an oak be defined as a 
kind of tree, for the name of a logical form, as 
" kind," can not be part of a real definition of a 
thing. 

5th. Not figurative. Figures indicate not what 
a thing really is, which is the aim of definition, but 
what it is like; as, gratitude is the memory of the 
heart. 

6th. Essential. (Section 6 d, 2nd.) The spe- 
cific difference must be an essential mark of the 
notion defined, as: plants and animals are living 
things ; and not an accidental mark, as : plants and 
animals are useful things. 

7th. Clear. If not, the purpose of the definition 
will be defeated, as when a net is defined as a reticu- 
lated texture with large interstices. 

8th. Short. That is, no longer than necessary. 
Too great brevity is also a defect, for it may destroy 
clearness. If all that is superfluous be omitted, and 
equally clear brief expressions be substituted for 
lengthy phrases, this end will be attained. A phrase 
or a clause may often be condensed. 

9th. Positive, if the notion defined be positive; 
negative, if that be negative. A negative definition 
of a positive notion, or the reverse, shows only what 
the notion is not, and not what it is, and is there- 
fore not a real definition. If a point be defined as 
position without magnitude, the specific difference 
is negative. But the negative notion, silence, is 



42 ESSENTIALS OF LOGIC 

properly defined as the absence (a negative term) 
of sound. 

PRACTICE ON SECTION 7 c 

1. Illustrate definition by any of the examples of 
correct division under the last head, pointing out 
in each case the genus and the specific difference. 

2. Show how each is a case of intersection, and that 
the part common to the two intersecting notions 
is the thing defined. 

3. Show that either of the two intersecting notions 
may be used as the genus in definition, and the 
other as the specific difference. 

4. Show that, therefore, there is a double subordi- 
nation in every case of correct definition. 

5. State each of the above definitions intensively. 

6. Select ten dictionary definitions for criticism. 

7. Test the following by the principles for correct 
definition. 

( 1 ) True knowledge is knowing how little we 
really do know. 

(2) A wise man is a fool who has found 
himself out. 

(3) An equilateral triangle is one whose sides 
and whose angles are equal. 

(4) An acute-angled triangle is one which has 
an acute angle. 

(5) Lead is a metal heavier than iron. 

(6) Cheese is a caseous preparation from 
milk. 

(7) A fallacy is an incorrect mode of rea- 
soning. 



NOTIONS 43 

(8) Conversion is changing the terms of a 
proposition. 

(9) A pump is a machine for raising water. 

(10) Man is a featherless biped. 

(11) An elephant is an animal that drinks 
through its nostrils. 

(12) Silence is the entire absence of sound. 

(13) Truth is that part of human thought 
which has proven correct. 

(14) Logic is the art of thinking. 

(15) A triangle is half a parallelogram. 

(16) Logic is the science of thought. 

(17) Mind is unextended substance. 

(18) A cur is a kind of dog. 

(19) Geometry is the science of extension. 

(20) Psychology is the science of mental life. 

(21) Psychology is the science of mind. 

(22) Psychology is the science of the phe- 
nomena of mind. 

(23) Psychology is the science of conscious- 
ness. 

(24) Thinking may be defined in one of its as- 
pects at least as the process of inter- 
preting the special by the general, or the 
new experience by the old. (Hibben.) 

(25) A moral being is one who has a con- 
science. 

(26) Evolution is a continuous change from 
indefinite incoherent homogeneity to defi- 
nite coherent heterogeneity of structure 
and function, through successive dil- 



44 ESSENTIALS OF LOGIC 

ferentiations and integrations. (Spen- 
cer.) 

(27) Capital is income-producing investment. 

(28) Wages is the price of labor. 

(29) Green is a color composed of blue and 
yellow. 

(30) A synopsis is an outline of a topic. 

(31) Motion is change of place. 

(32) Space is indefinite extension. 

(33) Dirt is matter in the wrong place. 

(34) Health is freedom from disease. 

(35) Wealth is accumulated property. 

(36) A sphere is a geometrical solid bounded 
by a surface every point of which is 
equally distant from a point within, called 
the center. 

(37) An angle is the space between two lines. 

(38) Conscience is that faculty of the soul 
which discerns right and wrong in con- 
duct. 

(39) A rocker is a chair with rockers. 

(40) A straight chair is a chair without rock- 
ers. 

(41) A plow is an instrument for cultivating 
the soil. 

(42) A house is a building to live in. 

(43) An animal is a brute or a human being. 

(44) An ostrich is a large swift bird that hides 
its head in the sand. 

(45) A story is an interesting account of an 
incident. 



NOTIONS 45 

(46) A peacock is a bird with brilliant plum- 
age. 
8. Correct any of the above that are defective. 



CHAPTER III 

THE PRIMARY LAWS OF THOUGHT 

8. Introductory. — If we think, we must use 
the notion and the judgment (Sections 3 and 5) ; 
that is, we must affirm or deny that two notions are 
in some one of the logical relations of Section 7. 
The necessity implied in the word, " must," is the 
essence of law, and the expression of what is neces- 
sary for correct thought constitutes the laws of 
thought. 

The two species, as " plant " and " animal," re- 
sulting from the dichotomy of a genus, as " living 
thing," are logical "contradictories," and can not 
co-exist in a thought about the same object. This 
opposition persists, of course, between any respective 
subordinate members of the original co-ordinate 
species, as " plant " and " dog," " potato " and " ani- 
mal," " potato " and " dog " ; but all these are ex- 
amples of opposition only within the limits of the 
class divided, and in the case of the last three pairs 
above, the opposition is still further limited. These 
last three and similar cases are not called contra- 
dictories, but contraries. 

Absolute contradictories are those that result from 
46 



PRIMARY LAWS OF THOUGHT 47 

logical division of the universe of things, as man 
and non-man, brute and non-brute, and the test is 
that every notion whatever belongs only to one 
class or to the other. Limited contradictories are 
those that result from the division of some genus 
lower than the highest, as man and brute ; these are 
contradictory only within the sphere of the divided 
genus, that is, every member of that genus belongs 
only to one or the other ; every animal is either man 
or brute. Contraries are pairs resulting from 
trichotomy or polytomy or from combinations like 
those in the above paragraph; no notion within the 
sphere of the class divided can belong to both of the 
contrary classes, but there are notions that belong 
to neither. 

It must be kept in mind that in logic we are deal- 
ing with the form of the thought, and not with the 
matter or with the language; and examples used to 
illustrate forms of thought must, therefore, be so 
worded as to show the form fully and clearly, and 
the logician has the right to make any change in the 
wording that will accomplish this end. 

9. The Law of Affirmation. — Any notion not 
contradictory to another notion may be affirmed of 
it. This law covers (1) the relation of co-exten- 
sion, or entire identity, as, all gems are jewels, or 
all jewels are gems; (2) the relation of subordina- 
tion, both from the point of view of the species, as, 
all base-balls are globes ; or from the point of view 



48 ESSENTIALS OF LOGIC 

of the genus, as, some globes are base-balls ; and this 
applies not only to species proximate to the genus, 
but to those further down the logical series, as in 
the above examples; (3) the relation of intersec- 
tion, which is merely a double subordination, as, 
man is an animal, and man is a rational being ; also, 
some animals are men, some rational beings are 
men. But the law does not forbid the affirmation 
of one of two notions, which are not contradictory 
(nor contrary), of the other, though the affirmation 
may not be true ; as, the earth is a cube, every man 
is a liar, no plant is good for food. The law, there- 
fore, does not establish truth, but merely forbids a 
specific error. 

10. The Law of Denial. — Any notion contra- 
dictory to another notion, must be denied of it. This 
law deals with the relation of co-ordination, includ- 
ing the limited contradictories and contraries, each 
within its proper sphere (Section 8) ; examples are: 
no' man is a brute ; no man is a horse ; no white man 
is a brute, or a horse ; no circle is square ; no lumin- 
ous body is non-luminous, etc. 

Apparent contradiction is often used to give point 
to real truth; as, make haste slowly; when I am 
weak, then am I strong. 

11. The Law of Exclusion. — Of two contra- 
dictory notions, one must be affirmed of any third 
notion. Or, any notion must be either affirmed or 
denied of any other notion. A is either B or non-B ; 



PRIMARY LAWS OF THOUGHT 49 

volcanoes are either in eruption or not in eruption; 
houses are either brick or not brick. If the contra- 
diction be not absolute (Section 8), then the "third 
notion " of the above law is limited to this lower 
genus, and the law is true only within the scope of 
that genus ; as, every animal is either man or brute. 
" Exclusion " means, therefore, that a third possi- 
bility is excluded. 

The laws of denial and exclusion may be com- 
bined and variously stated; as, of two contradic- 
tory notions, one must be affirmed, the other denied 
of any third notion ; or, any notion must be affirmed 
of one of two contradictory notions, and denied of 
the other. 

12. The Scope of the Laws. — Such are the 
primary laws of thought. From them are derived 
the many secondary laws and rules of logic. These 
laws do not establish truth. Their observance 
merely eliminates error in the form of the thought. 
We may reason correctly about false statements or 
non-existent things. What these laws and those 
derived from them forbid must be rejected; what 
they do not forbid may or may not be true; it is 
beyond the province of pure logic to decide. Logic, 
therefore, gives only negative and partial tests of 
error, and no positive criterion of truth. Truth de- 
pends on the matter of the thought. 



50 ESSENTIALS OF LOGIC 

PRACTICE ON SECTIONS 8 to 12 

1. Select from the following list pairs of (1) con- 
tradictories; (2) contraries: sharp, white, clear, 
alive, cowardly, obscure, dull, hard, dead, black, 
brave, soft. 

2. Name five other pairs of (1) absolute contra- 
dictories; (2) limited contradictories; (3) con- 
traries resulting from trichotomy or polytomy. 

3. Which of the following notions does the law of 

affirmation allow to be affirmed of the notion 
" cube " : round, square, pink, fragrant, spheri- 
cal, soft, conical, alive, costly, true? 

4. Which of the above list does the law of contra- 

diction require to be denied of the notion cube? 

5. Give five examples of apparent contradiction with 
real meaning. 

6. Complete the following according to the law of 
exclusion: food is wholesome or . . . ; govern- 
ments are monarchical or . . . ; everything is 
useful or . . . ; religions are true or . . . ; ani- 
mals are rational or . . . 

7. Which of the three kinds of pairs in 2 above il- 
lustrate exclusion? 

8. What point under this general head is illustrated 

by the following examples: 

(1) He was the lion of the party. 

(2) After he changed the figure, it was a 
circle with the corners square. 

(3) True knowledge is knowing how little 
we really do know. 



PRIMARY LAWS OF THOUGHT 51 

(4) His conduct is either foolish or crazy. 

(5) A wise man is a fool who has found him- 
self out. 

(6) He is beside himself. 

(7) His alter ego was responsible for that 
deed. 

(8) That was the wettest rain I ever was in. 

(9) He was so thin he could not tell whether 
he had the backache or the other kind. 

(10) I saw right through him. 

(11) He had reached a great height of hu- 
mility. 

(12) He was either at home or in his bedroom. 

(13) A liar told the truth. 

(14) There is one thief who never steals. 

(15) Here lies a man named "Miles," from 
Cincinnati, aged 59. 

(16) Iron is a very soft metal. Iron is hard. 
What is hard is soft. 

(17) It is decreed that you the enemy will 
slay. 

(18) He is a wise fool. 

(19) The friendship of the world is enmity 
with God. Friendship is enmity. 

(20) He that findeth his life shall lose it; and 
he that loseth his life for my sake shall 
find it. 

(21) But many that are first shall be last; and 
the last shall be first. 



CHAPTER IV 

PROPOSITIONS 

13. What Propositions are. — A judgment is 
an affirmation or a denial that one notion is con- 
tained in another, that the two are identical in whole 
or in part. Either marks are thought as contained 
in a concept or not; as plants are non-sentient, liv- 
ing, existing; or things are thought as contained in 
a class or not; as, plants are non-sentient living 
things. It is evident that the judgment deals with 
notions and their relations, and affirms or denies ac- 
cording to the primary laws of thought, the law of 
exclusion forbidding any third possibility. Also, 
when we remember that by abstraction we find that 
plants are non-sentient and living and existing, thus 
forming the concept, plant, we see that a judgment 
is primarily an explicit statement of what the con- 
cept already contains. We are, therefore, merely 
looking at things already familiar, but from a 
slightly different point of view. Concepts are judg- 
ments in a nutshell; judgments are the kernels of 
concepts. 

A proposition is a judgment expressed in language, 
and must therefore consist of the names of the two 

52 



PROPOSITIONS 53 

notions compared, and the verb affirming or denying 
their relation. The notion of which another is af- 
firmed or denied, is as in grammar called the sub- 
ject ; the other, the predicate. In strict logical form, 
affirmation is always made by the verb " is " or the 
plural, "are"; for the relation of the two notions 
is not dependent on time, but on their real nature, 
and general truth is expressed by the present tense. 
Denials are made only by " is not," and " are not." 
The " is " or " are " is called the copula, and " not " 
is said to qualify it ; every other word in the sentence 
belongs either to the subject or the predicate. Strict 
logical treatment requires every proposition to be 
put in the form, " subject is predicate," and any 
change in order or in expression which is necessary 
for arrangement in this form, must be allowed, the 
thought itself of course not being affected. As has 
been said, the subject and the predicate are also 
called the " terms " (Latin, terminus, end) of the 
proposition; and notions also are therefore called 
terms. 

Examples of propositions in strict form are : God 
is (i. e., is existing) ; water is necessary to life; the 
sum of the angles of a triangle is two right angles; 
the doctrine that the earth is the center of the uni- 
verse is not now held by astronomers. The sub- 
ject or the predicate may be a word, a phrase, a 
clause, or even a whole sentence; the subject, how- 
ever, is substantive, the predicate substantive or 



54 ESSENTIALS OF LOGIC 

adjective, according as the thought is extensive or 
intensive (Section 5, end). 

14. Kinds of Propositions. — Conditional 
propositions are those which (1) affirm the de- 
pendence of one of two propositions on the other, 
as, if land be rich and well- watered, it is fertile; or 
(2) affirm that one of two contradictories is true of 
some third notion, as, Cook either reached the North 
Pole or not; or (3) combine these two, as, if her 
husband dies, she will either marry again, or remain 
a widow. These forms are discussed in Section 23. 

Categorical propositions are those which affirm 
or deny without condition or alternative, as, rich 
and well- watered land is fertile; Cook reached the 
North Pole; Cook did not reach the North Pole. 

Simple categorical propositions are those which 
have only one independent subject and predicate ex- 
pressed or implied, as the examples in the last para- 
graph of Section 13; while compound propositions 
have more than one independent judgment expressed 
or implied ; as, gold is heavy and yellow, cotton and 
corn are raised in the South, he is their only friend, 
none but the brave deserve the fair, all but two were 
killed. For strict logical treatment, compound are 
resolved into simple propositions. The above ex- 
amples would yield the simple propositions: gold is 
heavy, gold is yellow, cotton is raised in the South, 
corn is raised in the South, he is their friend, no 
other than he is their friend, the brave deserve the 



PROPOSITIONS 55 

fair, no coward deserves the fair, nearly all were 
killed, two were not killed. 

A proposition simple in form, may be attended in 
mind by its opposite, and should in that case be 
treated as compound, and both components ex- 
pressed. If I say, some people are not selfish, with 
the emphasis on " some," I mean also, some are 
selfish, and the full expression of the thought re- 
quires both propositions. In speech, the mere tone 
or emphasis may be the only difference between com- 
pound and simple forms. 

The grammatically complex proposition, having 
subordinate clauses, is logically simple ; as, men who 
are eager to be rich are likely to be unscrupulous; 
this may be reduced to the simple form : men eager 
to be rich are likely to* be unscrupulous. 

15. Quality, Quantity, and Symbols of Prop- 
ositions. — Propositions affirm or deny, and are 
said to have affirmative or negative " quality." 
Care must be exercised to ascertain whether the 
negative belongs to the proposition, that is, to the 
copula, and not merely to the subject or the predi- 
cate ; especially as the transfer of the negative from 
copula to predicate or the reverse, is often easy. In 
" the universal cry was, no quarter," the negative 
belongs to the predicate, and the proposition is af- 
firmative; in " all is not gold that glitters," the nega- 
tive belongs with the " all," and the meaning is : 
" not all is gold that glitters," which, however, in 



56 ESSENTIALS OF LOGIC 

strict form becomes : " some things that glitter are 
not gold," and the proposition is negative; in " no 
news is good news," the negative belongs to the sub- 
ject, which is equivalent to " the lack of news," and 
the proposition is affirmative ; in " he is no gentle- 
man," the negative belongs grammatically to the 
predicate, " gentleman," though the proposition is 
obviously a logical denial. The positive and the 
negative aspects of a thought lie close together in 
the mind, yet the expression of the two is usually 
quite distinct, and we cannot say that the mere ex- 
pression of the one aspect implies the other, though 
we may have both in mind when we express only 
one. 

According to their " quantity," judgments are 
divided into "total" and "partial." Total judg- 
ments are those which affirm or deny the predicate 
of the whole subject; partial judgments, of only part 
of the subject; whether very little or nearly all, or 
however much, makes no difference in logic. The 
only distinction is that between the total, involving 
all, and the partial, involving only some of the sub- 
ject; with the relative magnitude of part and whole, 
logic has nothing to do. In strict form, every prop- 
osition begins either with " all," or an equivalent, 
(negative, " no," " none") ; or with " some " (neg- 
ative, " some . . . not "). 

Every thought must and does deal with either some 
or all of the subject, and if fully expressed, the 



PROPOSITIONS 57 

quantity would appear; but because of the customary 
omissions of speech, or through carelessness, it is 
not always possible to decide even from the context 
whether the subject be total or partial. It is not 
a question of what we would mean, but what the 
quantity was in the mind of the thinker. Of such 
cases we must judge according to our opinion of the 
probabilities, in fairness admitting the possibility of 
doubt. If in irritation some one says : men are 
fools, I judge him to mean some men, possibly only 
one; if some one says: boys will be boys, I judge 
the meaning to be all boys. 

Some of the w T ords indicating quantity are as 
follows : 

Total: a, an, all, always, any, both, each, every, 
individual name, name of substance, my, your, etc., 
the, this, that, etc., whoever, etc. ; with the nega- 
tives : neither, never, no, none, not any, nowhere. 

Partial: a, an, a few, a little, almost all, certain, 
many, most, nearly all, one, two, etc., some, some- 
times, somewhere, the, the majority, there are; with 
the negatives : all . . . not, few, hardly any, little, 
not all, not always, not every, rare, rarely, scarcely 
any, seldom, slight, small. 

It will be noticed that "a," " the," "all," 
" few," " little," appear in both lists. Examples 
of the double use are as follows: Total: a or the 
mule is a hybrid, all fixed stars are suns; partial 
affirmative: a few were saved, a little learning is a 



58 ESSENTIALS OF LOGIC 

dangerous thing, a or the mule is a tricky animal; 
partial negative: all trees are not pines, few were 
saved, little learning is thorough. 

Propositions whose subjects are individual or 
mathematical wholes (Section 7 b), are called in- 
dividual propositions, and are total; other total 
propositions whose subjects are classes, are called 
universal propositions. 

The division of propositions into affirmative and 
negative, and again into total and partial, gives 
four kinds, the total affirmative, the total negative, 
the partial affirmative, and the partial negative. 
Taking the first two vowels of " affirmo " (Latin, 
I affirm), the total affirmative is symbolized by A, 
the partial affirmative by I; while the vowels of 
nego (I deny) give E for the total negative, O 
for the partial negative. Examples are: 

A, All men are rational beings; E, No men are 
brutes ; I, Some men are blacksmiths ; O, Some men 
are not blacksmiths. 

Propositions whose predicates as well as their 
subjects are mathematical wholes, or quantities, are 
mathematical or quantitative propositions. As 
their subjects are always total, never partial, they 
are always symbolized by A or E, never I or O; 
as, the sun is the center of the solar system; x is 
equal to y; the sum of any two angles of a tri- 
angle is greater than the third angle. There is a 
class of propositions which may be viewed either 



PROPOSITIONS 59 

as mathematical or as compound: as, all present 
are all the members of this class, evidently mathe- 
matical as just defined, and yet resolvable into: all 
present are members, and, all members are pres- 
ent. 

PRACTICE ON SECTIONS 13 to 15 

The following list is purposely long, that different 
examples may be selected at different times, or for 
different classes. 1st. Put each proposition in strict 
logical form; 2nd, if compound, put each component 
in logical form; 3rd, affix to each the proper symbol, 
showing whether it be affirmative or negative, total 
or partial ; 4th, point out any that are individual, and 
any that are mathematical. 

1. Every mistake is not a proof of ignorance. 

2. All but one have disappeared. 

3. There's not a joy the world can give like that 

it takes away. 

4. Metals are all good conductors of heat. 

5. Nothing is beautiful except truth. 

6. Not many of the metals are brittle. 

7. There is no place like home. 

8. Not many, if any, metals are without luster. 

9. All gold mines cannot be wrought with profit. 

10. Heaven is all mercy. 

11. Romulus and Remus were twins. 

12. One kind of metal at least is liquid. 

13. Charity affords relief as far as possible. 

14. Few are acquainted with themselves. 

15. Some of our muscles act without volition. 



60 ESSENTIALS OF LOGIC 

16. God's word, exclusively, is to be received without 

question. 

17. Only citizens can hold property. 

18. Nearly all the troops have left the town. 

19. Only ignorant persons hold such opinions. 

20. Few persons are proof against temptation. 

21. Over the mountains poured the barbarian horde. 

22. Logic is only common sense formulated. 

23. Some students do not fail in anything, while all 

do not succeed. 

24. No illogical author is truly scientific. 

25. Not every man could stand such hardships. 

26. Work that cannot be paid for is alone worth 

doing. 

27. Necessity knows no law. 

28. All men are at times actuated by unselfish mo- 

tives. 

29. No one who is not a taxpayer can vote in this 

election. 

30. What can't be cured must be endured. 

31. Four years of study is required for a degree. 

32. Unasked advice is seldom acceptable. 

33. I shall not all die. 

34. There is none righteous, no, not one. 

35. They also serve who only stand and wait. 

36. He was too impulsive not to have committed 

many errors. 

37. Mankind are all men and women. 

38. A lie faces God, and shrinks from man. Bacon. 

39. There is no man doth a wrong for the wrong's 

sake. Bacon. 



PROPOSITIONS 61 

40. Prosperity is not without many fears and dis- 

tastes. Bacon. 

41. A man that is busy and inquisitive is commonly 

envious. Bacon. 

42. It is a miserable state of mind to have few things 

to desire and many things to fear. Bacon. 

43. To spend too much time in studies is sloth, to 

use them too much for ornament is affecta- 
tion, to make judgment wholly by their rules 
is the humor of a scholar. Bacon. 

44. Measure not dispatch by the times of sitting, 

but by the advancement of the business. 
Bacon. 

45. To choose time is to save time. Bacon. 

46. It never troubles the wolf how many the sheep 

be. Bacon. 

47. No people overcharged with tribute is fit for em- 

pire. Bacon. 

48. There is nothing makes a man suspect much 

more than to know little. Bacon. 

49. Certainly, the best mean(s), to clear the way 

in this same wood of suspicions, is frankly 
to communicate them with the party that 
he suspects. Bacon. 

50. The principal thing that hath been the destruc- 

tion of most plantations, has been the base 
and hasty drawing of profit in the first years. 
Bacon. 

51. As the baggage to an army, so is riches to vir- 

tue. Bacon. 

52. Of great riches there is no real use, except it 



62 ESSENTIALS OF LOGIC 

be in the distribution; the rest is but con- 
ceit. Bacon. 

53. Men mark when they hit, and never mark when 

they miss. Bacon. 

54. Nature is often hidden, sometimes overcome, 

seldom extinguished. Bacon. 

55. There be monks in Russia for penance, that will 

sit a whole night in a vessel of water, till 
they be engaged with hard ice. Bacon. 

56. Commonwealths and good governments do nour- 

ish virtue grown, but do not much mend the 
seeds. Bacon. 

57. No man prospers so suddenly as by others' er- 

rors. Bacon. 

58. There are a number of little and scarce dis- 

cerned virtues, or rather faculties and cus- 
toms, that make men fortunate. Bacon. 

59. Those who ascribe openly too much to their own 

wisdom and policy, end unfortunate. Bacon. 

60. Certainly there be, whose fortunes are like 

Homer's verses, that have a slide and easi- 
ness more than the verses of other poets. 
Bacon. 

61. They say that it is a pity the devil should have 

God's part, which is the tithe. Bacon. 

62. Some books are to be read only in parts; others 

to be read but not curiously (i. e., atten- 
tively) ; and some few to be read wholly, 
and with diligence and attention. Bacon. 

63. Histories make men wise; poets, witty; the 

mathematics, subtle; natural philosophy, 



PROPOSITIONS 63 

deep; moral, grave; logic and rhetoric, able 
to contend. Bacon. 

64. Some men's behavior is like a verse, wherein 

every syllable is measured. Bacon. 

65. To praise a man's self cannot be decent, except 

it be in rare cases. Bacon. 

66. Bismarck was a great statesman. 

6y. Bismarck was the greatest statesman of his time. 

68. The fear of the Lord is to hate evil. Bible. 

69. There is that speaketh like the piercings of a 

sword. Bible. 

70. The eyes of the Lord are in every place, be- 

holding the evil and the good. Bible. 

71. He that loveth pleasure shall be a poor man. 

Bible. 
J2. He that hath no rule over his own spirit is like 
a city that is broken down and without walls. 
Bible. 

73. A whip for the horse, a bridle for the ass, and 

a rod for the fool's back. Bible. 

74. As a mad man who casteth firebrands, arrows, 

and death, so is the man that deceiveth his 
neighbor, and saith, Am I not in sport? 
Bible. 

75. Where no wood is, there the fire goeth out: so 

where there is no talebearer, the strife ceas- 
eth. Bible. 

76. He that by usury and unjust gain increaseth his 

substance, he shall gather it for him that 
will pity the poor. Bible, 
yy. Though he heap up silver as the dust, and pre* 



64 ESSENTIALS OF LOGIC 

pare raiment as the clay; he may prepare 
it, but the just shall put it on, and the inno- 
cent shall divide the silver. (Said of the 
"wicked man.") Bible. 

78. The wealth of the sinner is laid up for the just. 

Bible. 

79. For God giveth to a man that is good in his 

sight wisdom, and knowledge, and joy: but 
to the sinner he giveth travail, to gather 
and to heap up, that he may give to him that 
is good before God. Bible. 

80. The words of wise men are heard in quiet more 

than the cry of him that ruleth among fools. 
Bible. 

81. Not every one that saith unto me, Lord, Lord, 

shall enter into the kingdom of heaven; but 
he that doeth the will of my Father which 
is in heaven. Bible. 

82. Nature, like liberty, is but restrained 

By the same laws which first herself ordained. 
Pope. 

83. Nor is it Homer nods, but we that dream. Pope. 

84. Of all the causes which conspire to blind 
Man's erring judgment, and misguide the mind, 
What the weak head with strongest bias rules, 
Is pride, the never-failing voice of fools. Pope. 

85. {Some to church repair, 

Not for the doctrine, but the music there. Pope. 

86. Some ne'er advance a judgment of their own, 
But catch the spreading notion of the town: 
They reason and conclude by precedent. 



PROPOSITIONS 65 

And own stale nonsense which they ne'er invent. 
Some judge of authors' names, not works, and 

then 
Nor praise nor blame the writings, but the men. 

Pope. 

87. Some praise at morning what they blame at 

night ; 
But always think the last opinion right. Pope. 

88. Fondly we think we honor merit then, 

When we but praise ourselves in other men. 
Pope. 

89. All seems infected that th' infected spy, 

As all looks yellow to the jaundiced eye. Pope. 

90. In human works, though labored on with pain, 
A thousand movements scarce one purpose gain ; 
In God's, one single can its end produce ; 

Yet serves to second too some other use. Pope. 

91. Tis but a part we see, and not a whole. Pope. 

92. And who but wishes to invert the laws 

Of Order, sins against the Eternal Cause. Pope. 

93. And if each system in gradation roll 
Alike essential to the amazing whole, 
The least confusion but in one, not all 

That system only, but the whole must fall. 
Pope. 

94. All nature is but art, unknown to thee; 

All chance, direction, which thou canst not see; 

All discord, harmony not understood; 

All partial evil, universal good; 

And spite of pride, in erring reason's spite, 

One truth is clear, Whatever is, is right. Pope, 



66 ESSENTIALS OF LOGIC 

95. Love, hope, and joy, fair pleasure's smiling 

train, 
Hate, fear, and grief, the family of pain, 
These mixed with art, and to due bounds con- 
fined, 
Make and maintain the balance of the mind. 
Pope. 

96. The merchant's toil, the sage's indolence, 
The monk's humility, the hero's pride, 

All, all alike, find reason on their side. Pope. 

97. Fixed to no spot is happiness sincere, 

'Tis nowhere to be found, or everywhere : Pope. 

98. Who thus define it, say they more or less 
Than this, that happiness is happiness? Pope. 

99. To whom can riches give repute, or trust, 
Content, or pleasure, but the good and just? 

Pope. 

100. Who wickedly is wise, or madly brave, 

Is but the more a fool, the more a knave. Pope. 

1 01. He has no hope who never had a fear. Cowper. 

102. Seldom, alas ! the power of logic reigns 

With much sufficiency in royal brains; Cowper. 

103. The diadem, with mighty projects lined, 
To catch renown by ruining mankind, 

Is worth, with all its gold and glittering store, 
Just what the toy will sell for, and no more. 
Cowper. 

104. There is no one who feels anger where the object 

seems impracticable to his revenge. Aristotle. 

105. To overcome is pleasant, not to the ambitious 

only, but even to all. Aristotle. 



PROPOSITIONS 67 

106. Neither splendor of vestments, nor preeminence 

of beauty, nor the amount of gold, con- 
tributes so much to the commendation of a 
woman as good management in domestic af- 
fairs, and a noble and comely manner of life. 
Aristotle. 

107. He is free who lives as he likes ; who is not sub- 

ject to compulsion, to restraint, or to vio- 
lence. Epictetus. 

108. The cause of all human evils is the not being able 

to apply general principles to special cases. 
Epictetus. 

109. No living being is held by anything so strongly 

as by its own needs. Epictetus. 

no. Eloquence is a gift not of mind only, but of lungs 
and strength. Cicero. 

in. Except among the virtuous friendship cannot ex- 
ist. Cicero. 

112. Friendship is nothing else than a complete union 

of feeling on all subjects, divine and human. 
Cicero. 

113. To whom can life be worth living, who does not 

repose on the mutual kind feeling of some 
friend? Cicero. 

114. We do not use fire and water on more occasions 

than we do friendship. Cicero. 

115. Just as a man has most confidence in himself, 

and as he is most completely fortified by 
worth and wisdom, so that he needs no one's 
assistance, and feels that all his resources 
reside in himself, in the same proportion he 



68 ESSENTIALS OF LOGIC 

is most highly distinguished for seeking out 
and forming friendships. Cicero. 

116. There is no greater enemy to friendship than 
covetousness of money. Cicero. 

ii J. Not only is fortune blind herself, but she com- 
monly renders blind those whom she em- 
braces. Cicero. 

1 1 8. No one person ever was so dear to another as 

you are to the people of Rome. Seneca (to 
Nero). 

119. Trifling evils may cheat us and elude our ob- 

servation, but we gird up our loins to attack 
great ones. Seneca. 

120. It often happens, that even when they (orators 

who are bad men) speak the truth, belief is 
not accorded them. Quintilian. 

121. The idle man excuseth him in winter because of 

the great cold, and in summer then by reason 
of the heat. Chaucer. 

122. Honor is nothing else but to do reverence to 

another person for the good and virtuous dis- 
position that is in him. Caxton. 

123. Ofttime battle is advanced more for getting of 

silver than by the force and strength of men. 
Caxton. 

124. There is no man so assured of his honor, of his 

riches, health, or life but that he may be de- 
prived of either, or all, the very next day 
or hour to come. Raleigh. 

125. There are no fewer forms of minds than of bod- 

ies amongst us. Jonson. 



PROPOSITIONS 69 

126. Some are fit to make divines, some poets, some 

lawyers, some physicians, some to be sent to 
the plow, and trades. Jonson. 

127. There be some that are forward and bold; and 

these will do every little thing easily. These 
never perform much, but quickly. They are 
what they are on the sudden; they show 
presently like grain that, scattered on the top 
of the ground, shoots up, but takes no root; 
has a yellow blade, but the ear empty. Jon- 
son. 

128. There want not men of equal authority and 

credit, that prefer action to be the more ex- 
cellent (of the two, action and contempla- 
tion). Walton. 

129. There is nothing strictly immortal but immor- 

tality. Browne. 

130. Revolutions of ages do not oft recover the loss 

of a rejected truth. Milton. 

131. But when God hath decreed servitude on a sin- 

ful nation, fitted by their own vices for no 
condition but servile, all estates of a govern- 
ment are alike unable to avoid it. Milton. 

132. That infection which is from books of contro- 

versy in religion is more doubtful and dan- 
gerous to the learned than to the ignor- 
ant. Milton. 

133. Many boys are muddy-headed till they be clari- 

fied with age, and such afterward prove the 
best. Fuller. 

134. All the whetting in the world can never set a 



70 ESSENTIALS OF LOGIC 

razor's edge on that which hath no steel in 
it. Fuller. 

135. No man is more miserable than he that hath no 

adversity. Taylor. 

136. Of all mankind there are none so shocking as 

these injudicious civil people. Steele. 

137. Any affectation whatsoever in dress implies in 

my mind a flaw in the understanding. Ches- 
terfield. 

138. Good manners are to particular societies what 

good morals are to society in general. Ches- 
terfield. 

139. Men who converse only with women are friv- 

olous, effeminate puppies, and those who 
never converse with them are bears. Chester- 
field. 

140. No man is ridiculous for being what he really is, 

but for affecting to be what he is not. 
Chesterfield. 

141. Nothing appears more surprising to those who 

consider human affairs with a philosophical 
eye than the easiness with which the many 
are governed by the few. Hume. 

142. When men act in a faction, they are apt, without 

shame or remorse, to neglect all the ties of 
honor and morality, in order to serve their 
party. Hume. 

143. This fierce spirit of liberty is stronger in the 

English colonies probably than in any other 
people of the earth. Burke. 

144. How seldom, friend, a good great man inherits 



Propositions ft 

Honor or wealth with all his worth and pains! 
Coleridge. 

145. It seems little to be perceived, how much the great 

Scriptural idea of the worldly and the un- 
worldly is found to emerge in literature as 
well as in life. De Quincey. 

146. There is always hope in a man that actually and 

earnestly works; in Idleness alone is there 
perpetual despair. Carlyle. 

147. Judgment for an evil thing is many times de- 

layed some day or two, some century or two, 
but it is sure as life, it is sure as death. 
Carlyle. 

148. Among mental as among bodily acquisitions, the 

ornamental comes before the useful. Spen- 
cer. 

149. Whatsoever every man chiefly loves above all 

other things, that he persuades himself is 
best for him. Boethius. 

150. There is no one that has not need of some addi- 

tion, except God alone. Boethius. 

151. How can that be evil which the mind of every 

man considers to be good, and strives after, 
and desires to obtain? Boethius. 

152. Many people show gratitude for trifling, but there 

is hardly one who does not show ingratitude 
for great favors. Rochefoucauld. 

153. A man thinking or working is always alone, let 

him be where he will. Thoreau. 

154. No ceremony that to great ones 'longs, 

Not the king's crown nor the deputed sword, 



72 ESSENTIALS OF LOGIC 

The marshal's truncheon nor the judge's robe, 
Become them with one-half so good a grace 
As mercy does. Shakespeare. 

155. In law, what plea so tainted and corrupt 
But, being seasoned with a gracious voice, 
Obscures the show of evil? Shakespeare. 

156. There is no vice so simple but assumes 

Some mark of virtue on his outward parts. 
Shakespeare. 

157. Our remedies oft in ourselves do lie, 
Which we ascribe to heaven. Shakespeare. 



PART II 
DEDUCTIVE INFERENCE 



CHAPTER V 

IMMEDIATE DEDUCTION 

1 6. Nature and Kinds of Inference. — As to 

their origin, judgments are of two kinds, psycho- 
logical, called intuitions; logical, called inferences. 
Intuitions are not derived from other judgments, 
but are primary facts of consciousness, known 
through the senses or by the intellect; as the pri- 
mary laws of thought, the judgment that I exist, 
that I see color, hear sound, etc. Inferences are 
judgments derived from one or more other judg- 
ments; as when from, all men are animals, we in- 
fer, some animals are men ; or from, no Greeks are 
barbarians, and Socrates is a Greek, we infer, Soc- 
rates is not a barbarian. Intuitions may be and 
often are the judgments from which inference is 
made; but the intuition is not a thought, only the 
inference is a thought. 

There are two kinds of inference, that from a 
judgment concerning some of a notion to a judg- 
ment concerning all of the notion, as when from 
the judgment based on experience, that some gold 
melts at 1200 degrees, we infer that all gold melts 
at 1200 degrees. This inference from some to all 

75 



^6 ESSENTIALS OF LOGIC 

is inductive inference, and is discussed in Part III 
below. 

The other kind of inference, called deduction, 
infers from all to all, all to some, or some to some 
of the notion; and it is evident that induction and 
deduction include all possible inferences. Ex- 
amples of deduction are the inference from, no iron 
is soft, to, no soft thing is iron; from, all iron is 
hard, to, some hard things are iron ; and from some 
iron is brittle, to, some brittle things are iron. 

These examples are all cases of immediate de- 
duction, that is, deduction without a medium, or 
third notion; only the same two notions being used 
in the original judgment and in the inference de- 
rived from it. Mediate deduction is considered in 
the next chapter. 

Sometimes a judgment is implied with or in an- 
other, and might seem to be an inference, when it 
is really not a new judgment, but already thought 
more or less obscurely with the other. Logicians 
differ here, but we are at liberty to decide what we 
shall exclude from the class we have called in- 
ferences, so long as no principle is violated. All 
such cases might be included among inferences, but 
it is simpler to limit inference as much as we may 
without manifest error. It is hardly to be said 
that from, John strikes Henry, we infer, Henry is 
struck by John; or, if I say, O yes, some men are 
honest, implying by emphasis on " some " that some 



IMMEDIATE DEDUCTION yy 

are not honest, the latter is not inferred from the 
former, but thought along with it; it is not infer- 
ence to say that because man is mortal then man is 
a mortal being, or the reverse; nor that because 
James is the son of Joe, therefore Joe is the father 
of James. There is in such cases no real progress 
of thought, and we shall therefore not count as in- 
ferences (i) the change from active to equivalent 
passive, and the reverse; (2) the judgment thought 
together with another, even if not fully expressed 
or indicated; (3) the change from intensive to ex- 
tensive thought, or the reverse; (4) the transfer of 
the thought from one of two correlatives to the 
other. 

Finally, as has been said, deductive inference can 
not pass from some to all, but only from all to all, 
all to some, and some to some of a notion. In 
other words, in deduction the quantity of a term 
can not be increased. 

17. Methods of Immediate Inference. The 
question now arises, by what legitimate methods 
may we pass immediately from one judgment to 
another. There are four general ways : 

1st. Method. By Combination. The two terms 
of the given judgment may be combined each with 
the same mark or concept, or with strictly equiva- 
lent marks or notions, thus forming a new judg- 
ment. If a house be a building then, a brick house 
is a brick building; if law be just, then legal ac- 



78 ESSENTIALS OF LOGIC 

tion is just action; if a college be an institution for 
higher education, and if definite entrance require- 
ments are beneficial to the schools, then, a college 
with definite entrance requirements is an institu- 
tion for higher education with something beneficial 
to the schools. So, too, may judgments be sep- 
arated into equivalent components, but only when 
the same mark is taken from both terms; for the 
equivalence of other elements than marks is not 
known from the judgment itself. In either case, 
absolute equivalence must be the rule. For ex- 
ample, a mouse is an animal, but a large mouse is 
not a large animal; a carpenter is a citizen, but 
a bad carpenter is not therefore a bad citizen. This 
is usually called " determination." 

2nd. Method. By Contradiction. By the pri- 
mary laws of thought (Section 8), if a notion be 
affirmed of another, its contradictory must be de- 
nied of that other, and the reverse. For example, 
if animals are mortal, it follows that animals are 
not immortal ; if some men are easy to please, then 
some men are not hard to please; if no member of 
this class is late, then every member of this class is 
on time; if some people are not honest, then some 
are dishonest* Thus each of the four propositions 
A, I, E, O, as illustrated above, will by this process 
yield a new form, equivalent to the old in essen- 
tial meaning, yet a different form of thought, an 
inference. For when, for example, we say, ani- 



IMMEDIATE DEDUCTION 79 

mals are mortal, we affirm animals to be contained 
is the class, mortal beings; but when we say, ani- 
mals are not immortal, we do not affirm this, but 
deny that they are in the opposite class, immortal 
beings. The two thoughts may be together in 
mind, but they are not identical, either being an in- 
ference from the other. 

This kind of immediate inference is sometimes 
called inrmitation, sometimes obversion. 

3rd. Method. By Conversion. If one notion, 
the subject, be related to another, the predicate; 
then the predicate must be in some relation to the 
subject, and that relation may be affirmed by re- 
versing the proposition, that is, by exchanging its 
subject and predicate. But, as the predicate of an 
affirmative is not totally involved, it can not be- 
come the subject of a total proposition; while the 
predicate of a negative being totally involved may 
be the subject of a total proposition. The process, 
which is called " conversion," has three varieties, 
as follows : 

First, Simple Conversion. If no misers are happy 
men, then no happy men are misers; if some trees 
are living things, then some living things are 
trees. This simple exchange of subject and predi- 
cate is applicable to E, for both subject and predi- 
cate of E are total ; it is applicable to I, for both sub- 
ject and predicate of I are partial ; it is not applicable 
to A, for the subject of A is total and the predicate 



8o ESSENTIALS OF LOGIC 

partial ; nor to O, for the subject of O is partial and 
the predicate total. 

Second, Conversion by Limitation. The proposi- 
tion, all crows are birds, affirms the identity of the 
subject, crows, with only part of the predicate, 
birds; that is, we can not say from this statement 
whether or not all birds are meant, and must there- 
fore " limit " the inference as to birds to, some 
birds are crows, and the judgment originally total 
becomes " by limitation " partial. This is also 
named conversion " per accidens." It may be ap- 
plied to E, giving O, but as E will give E by sim- 
ple conversion, it would be absurd to apply this 
method, when more general truth can be attained 
by the other. It is therefore especially applicable 
to A. 

Third, the Conversion of O. The truth is, O 
can not be converted, for it would give O, a nega- 
tive with a total predicate, and the subject of the 
original proposition is partial and can not there- 
fore be predicate of O. A similar difficulty in the 
case of A was overcome just above by reducing 
the quantity of the subject from total to partial, 
but the trouble here is with the quantity of the 
predicate, and as the predicate of a negative is al- 
ways totally denied, there is no way of reducing 
that, except by changing the proposition to an 
affirmative. This is done by the method of using 
the contradictory (2nd. Method above), which 



IMMEDIATE DEDUCTION 81 

gives I, and this can then be converted simply. For 
example, if some engines are not locomotives, we 
can not say, therefore some locomotives are not 
engines; because excluding only some engines from 
the class, locomotives, does not prevent locomotives 
from being included in some other part of the class, 
engines. So we adopt the method described above, 
the use of the contradictory predicate giving, some 
engines are non-locomotives, and simple conversion 
of this giving, some non-locomotives are engines. 

This is sometimes called conversion by contra- 
position, but it is evidently not a new method, as 
shown above. It may be applied to A, as well as to 
O. 

As a predicate must be either a mark or a class, 
a proposition with an individual subject, such as, 
Brutus was an assassin, or the earth is a sphere, can 
not be converted, for the subject of the individual 
proposition is neither a mark nor a class, and can 
not become a predicate. The words may be turned 
around, but the thought is not reversed. 

4th. Method. By the Relation of Propositions. 
Any two of a set of the four kinds of propositions, 
A, E, I, O, with the same subject and predicate, 
bear certain fixed relations to each other, such that 
the truth or the falsity of one involves the truth or 
the falsity of others. For example, if all grass be 
green, then it is true that some grass is green, but 
false that no grass is green, and that some grass is not 



82 ESSENTIALS OF LOGIC 

green; that is, if A be true, I is true, but E and O 
are false. Again, if no man be perfect, it is true 
that some men are not perfect, but false that all 
men are perfect, and that some men are perfect; 
that is, if E be true, O is true, but A and I are 
false. Still again, if some fruits be food, it is false 
that no fruits are food, and undetermined as to, 
all fruits are food, and, some fruits are not food; 
that is, if I be true, E is false, but A and O are 
undetermined. Lastly, if some animals be not 
bipeds, it is false that all animals are bipeds, and 
undetermined as to, no animals are bipeds, and, 
some animals are bipeds; that is, if O be true, A is 
false, and O and I are undetermined. 

Similarly it will be found that if A be false, O is 
true, E and I undetermined; if E be false, I is true, 
A and O undetermined; if I be false, E and O are 
true, A false; and if O be false, A and I are true, 
E false. 

It appears from the above examination that (i) 
of the two pairs, A and O, E and I, one proposition 
in either pair is always true, the other false; ac- 
cording to the primary laws (Sections 10, n), 
these are " contradictories ; " (2) of the pair, A 
and E, both can not be true, but both may be false, 
and they are called "contraries;" for they are in 
the same relation as any pair of the members of a 
trichotomy or polytomy (Section 7 b), which ex- 
clude each other but leave a third class, or more ; as 



IMMEDIATE DEDUCTION 83 

a tree can not be both oak and pine, but may be 
neither; (3) of the pair I and O, both may be true, 
but both can not be false, and they are called " sub- 
contraries ; " (4) of the pairs A and I, E and O, 
if the universal be true, the particular is true; if the 
particular be false, the universal is false; I and O 
are " subalternate " respectively to A and E. 

Successive application of the above principles to 
a proposition would produce many derived forms. 
The following are some of these: 

First : " Controversion," sometimes called 
"contraposition," is obversion (Section 17, 2nd. 
Method) followed by conversion, of A, E, or O. 

Second : " Contraposition " is obversion, con- 
version, then obversion again, of A, E, O; or it is 
contraversion followed by obversion. 

Third : " Inversion " is contraposition followed 
by conversion, then obversion, of A, or E. The 
resulting proposition has for subject the contra- 
dictory of the original subject, and for predicate the 
contradictory of the original predicate. The vari- 
ous steps indicated are necessary to prove the cor- 
rectness of the process, but once proven, we may 
pass to the inverse form directly. A gives I; E 
gives O. 

17 a. Immediate Inference of Mathematical 
Propositions. — The mathematical proposition 
has both subject and predicate always total, never 
partial. It follows that the principle of combina- 



84 ESSENTIALS OF LOGIC 

tion of Section 17 reduces to the familiar axioms: 
if equals or unequals be added to equals (or sub- 
tracted from them, etc.) the results are equals or 
unequals, respectively. 

The principle of using the contradictory applies 
only in that if two quantities be equal, they are not 
unequal, and the reverse. 

Finally, subject and predicate both being always 
total, the mathematical proposition may always be 
converted simply. The sun is the center of the 
solar system, therefore the center of the solar sys- 
tem is the sun ; x is equal to y, therefore y is equal to 
x; the sum of any two angles of a triangle is greater 
than the third angle, therefore any angle of a tri- 
angle is less than the sum of the other two angles. 

PRACTICE ON SECTIONS 16 and 17 

Using any of the examples for practice in the pre- 
ceding section, first reduced to simple propositions in 
strict logical form, copious practice should be had 
under the following heads: 

1. Select some suitable mark, and form a new judg- 

ment by combining it with the two terms of any 
proposition. 

2. Combine assigned pairs of suitable propositions, 

such as Nos. 5 and 16, 17 and 41, 2.2, and 24, 40 
and 41, 71 and y2. 

3. Deny the contradictory of any simple proposi- 

tion (i. e. " infmitate " it, or give its " obverse "). 



IMMEDIATE DEDUCTION 85 

4. Convert simply any that admit of simple conver- 

sion. 

5. Convert by limitation any convertible only in that 

way. 

6. Convert any partial negative (O) by infinitating 

and then converting simply (i. e. by " contra- 
position "). 

7. Convert by any of the above methods, and as 

many as are applicable, any examples assigned. 

8. Select any proposition. If it be true, are the other 

three (of A, E, I, O) with the same subject 
and predicate, true or false? 

9. Suppose each one selected to be false. Are the 

other three true or false, as above? 

10. Contravert any assigned. 

11. Invert any assigned, in some showing each step, 

in others directly. 



CHAPTER VI 

MEDIATE DEDUCTION 

1 8. Nature of Mediate Inference. — Mediate 
inference is inference through a medium, or " mid- 
dle 'term." Three notions are used, and not only- 
two, as in immediate inference. The two notions 
which are being investigated, are each compared 
with the third notion, and as a result of the compari- 
son, their relation to each other is determined. 
For example, all true statesmen are servants of the 
state rather than of self, most politicians are not 
servants of the state rather than of self, therefore, 
most politicians are not true statesmen. Not being 
able, perhaps, to judge immediately of the relation 
of the two notions, true statesmen, and most poli- 
ticians, each is compared with the third notion, serv- 
ants of the state rather than of self, and one be- 
ing found to agree with this, the other not, the two 
are therefore judged not to agree with each other. 

19. The Syllogism and its Parts. — The full 
expression of a mediate inference is called a " syl- 
logism," and evidently requires three propositions. 
The two in which the middle term occurs are called 
the " premises " ; the third, in which the two no- 

86 



MEDIATE DEDUCTION 87 

tions under investigation are compared, is the " con- 
clusion " (Latin, shut up together). The subject 
of the conclusion is called the " minor " term, be- 
cause it is affirmed or denied to be contained in the 
predicate, which is therefore the " major " term. 
The premise in which the major term is compared 
with the middle term, is called the major premise; 
that in which the minor and the middle are com- 
pared, the minor premise. 

The order of the propositions is unimportant, but 
for convenience in logical study, the order, major, 
minor, conclusion, is adopted. 

20. Rules of the Syllogism. — Some of the 
following rules are based on what has just been 
said, the others have additional reasons given. 

First. Every syllogism has three terms and no 
more. It we should compare the major and the 
minor terms with two other different terms, no 
conclusion could be drawn. Even the same word 
or group of words with different meanings, would 
count as two terms, and make the total four, just 
as if two different words were used; for the term 
is not the mere words, but the real meaning. An 
example is: school children are pupils, pupils are 
part of the eye, therefore school children are part 
of the eye. 

Second. Every syllogism has three propositions, 
and no more. This is evident from the nature of 
the syllogism. 



88 ESSENTIALS OF LOGIC 

Third. The middle term must be total (or, " dis- 
tributed ") in at least one of the premises. For 
if we compare the major term with only part of 
the middle, and the minor term with only part, the 
two parts might be entirely distinct, and no con- 
clusion would follow. This would be equivalent 
to having four terms. If chairs be seats, and 
benches be seats, we can not conclude that chairs 
are benches, for we have used in each premise only 
part of the class, seats, and the parts may be, and 
in this case are distinct; nor, for the same reason, 
if spheres be round things, and balls be round 
things, can we conclude that balls are spheres, 
though we know it be true. 

Violation of this principle is called " undistributed 
middle." 

Fourth. No term may be total in the conclusion, 
unless total in a premise. For that would be to 
conclude about all of a term from a judgment 
about only some of it. It is important to remem- 
ber here that the subjects of A and E, and the predi- 
cates of E and O, are always total, or " distributed/' 
while terms in other positions are partial, or " un- 
distributed." 

Violation of this principle is called the " illicit 
process," or proceeding illegally from some to all in 
thought. If from, all statesmen are patriots, and 
no self-seekers are statesmen, we conclude, no self- 
seekers are patriots, the major term, patriot, is par- 



MEDIATE DEDUCTION 89 

tial in the premise and total in the conclusion, and 
the reasoning is fallacious, though the conclusion 
is true. This is " illicit major," and can evidently 
occur only when the conclusion is negative. If 
from, no self-seekers are statesmen, and some self- 
seekers are politicians, we conclude, no politicians 
are statesmen, the fault is " illicit minor," and evi- 
dently can occur only when the conclusion is total. 

Fifth. If both premises be negative, no conclu- 
sion follows. For if neither the major nor the 
minor term agrees with the middle, we can not 
judge their relation to each other. 

Sixth. If one premise be negative, the conclusion 
is negative. For then either the major or the minor 
agrees with the middle term, and the other dis- 
agrees, so that they must disagree with each other, 
which means the conclusion is negative. 

To sum up briefly: 

Rule 1. A syllogism has three terms, three 
propositions, and at least one affirmative premise. 

Rule 2. If one premise be negative, the conclu- 
sion is negative. 

Rule 3. The middle term must be total at least 
once. 

Rule 4. A term total in the conclusion, must be 
total in the premise. 

The above four rules constitute the sufficient test 
of syllogistic reasoning. The general principle jus- 
tifying the syllogism may be derived as follows: 



90 ESSENTIALS OF LOGIC 

By the law of affirmation (Section 9) a notion 
not contradictory to another may be affirmed of it; 
by the law of denial a notion contradictory to an- 
other must be denied of it. From these laws it fol- 
lows that if two notions agree with a third, so that 
all of the third is involved once (Rule 3 above) 
they agree with each other; also that if one of the 
two agrees with the third, and the other not (Rule 
2 above), so that the whole of the third is involved 
once, then they disagree with each other ; and lastly, 
if neither agrees with the other (Rule 1 above), 
nothing can be concluded as to their agreement with 
each other. 

These principles are evidently equivalent to the 
four rules of the above summary. It is of course 
evident, also, that any notion may be substituted for 
an equivalent notion. 

21. Syllogisms Incompletely Expressed. — 
Complete expression of syllogistic reasoning is rare 
in the actual conveyance of thought, obvious parts 
being left to the mind of the reader or hearer to 
supply; yet for the purpose of critical examination 
of the thought, the full form is often necessary. 
Incomplete syllogisms are called " enthymemes " 
(Greek, in the mind). The logician has of course 
the right to full expression. 

The kind of enthymeme most common in or- 
dinary interchange of thought, and far more com- 
mon than the fully expressed syllogism, omits one 



MEDIATE DEDUCTION 91 

of the three propositions of the syllogism, the omit- 
ted member being readily supplied from general 
knowledge or from specific circumstances. If we 
say, all braggarts are cowards, Falstaff is a brag- 
gart, therefore Falstaff is a coward, the syllogism 
is complete; but if we say only, Falstaff is a cow- 
ard, for he is a braggart, we have an enthymeme, 
for the major premise is " in the mind " ; or if we 
say, Falstaff is a coward, because all braggarts are 
cowards, the minor premise is " in the mind " ; or, 
finally, if we say, all braggarts are cowards, and 
Falstaff is a braggart, the conclusion is " in the 
mind." 

Less common, but still often used, is the en- 
thymeme with two propositions omitted, the major 
premise being the one expressed, in nearly, if not 
quite every instance, and the minor being usually, if 
not always, suggested by the actual circumstances. 
A proverb or other popular saying, any general 
statement by way of insinuation, epitaphs, etc., may 
be the major premise o<f the enthymeme of only one 
expressed proposition. Hearing of an attempt on 
the life of a ruler, we say, " uneasy lies the head 
that wears a crown " ; the minor premise, the head 
of this ruler wears a crown, being suggested at 
once. Seeing a clumsy effort to do something more 
easily done otherwise, we say, " lazy people take 
the most trouble " ; the other propositions being ob- 
vious. 



92 ESSENTIALS OF LOGIC 

22. Series of Syllogisms. — Reasoning is sel- 
dom limited to one mediate inference, but is con- 
tinued through a series of connected syllogisms, the 
conclusion of one becoming a premise of the next, 
as any conclusion may. The syllogism of which 
the repeated proposition is the conclusion, is the 
" prosyllogism," the syllogism of which it is a prem- 
ise, is the " episyllogism." Usually only one prem- 
ise of the prosyllogism is expressed, and it is 
therefore an enthymeme. For example: vice is 
odious, and avarice is vice, for it makes men slaves ; 
therefore avarice is odious. Here the minor prem- 
ise is the conclusion of a prosyllogism whose 
minor premise, avarice makes men slaves, is ex- 
pressed, but whose major premise, whatever makes 
men slaves is a vice, is " in the mind." Both prem- 
ises of the episyllogism may be supported in this 
way, and the full expression of the reasoning in 
that case would require three syllogisms; as if above 
we had said : vice is odious, for whatever exalts the 
animal above the moral is odious. The name " epi- 
chirema" has been given to the reasoning when 
limited to one pair of pro- and episyllogism ; " dou- 
ble epichirema " to the case where each of the two 
premises of the same episyllogism is supported by a 
prosyllogism. 

If this relation of prosyllogism and episyllogism 
be continued through several syllogisms, the result- 
ing chain is called a "sorites" (Greek, heap). 



MEDIATE DEDUCTION 93 

Thus, the prudent are temperate, the temperate are 
constant, the constant are unperturbed, the unper- 
turbed are happy, therefore the prudent are happy. 
While this reasoning may be fully expressed in a 
series of pro- and episyllogisms, the mind does not 
in the actual process stop to form the various in- 
termediary conclusions, but runs through the suc- 
cessive middle terms easily and naturally, sees that 
each wholly contains the next, and concludes finally 
that the first term agrees or not with the last. The 
separate syllogisms would be as follows: first, the 
prudent are temperate, the temperate are constant, 
therefore the prudent are constant; second, the pru- 
dent are constant, the constant are unperturbed, 
therefore the prudent are unperturbed; and so on 
to the end. The arrangement of premises may be 
reversed: the unperturbed are happy, the constant 
are unperturbed, the temperate are constant, the 
prudent are temperate, therefore the prudent are 
happy. 

In the first form, the last premise may be nega- 
tive; in the second form, of course, the first prem- 
ise; if any other be negative, illicit process would re- 
sult. In the first form, the first premise may be 
partial; in the second form, the last premise; if any 
other be partial, undistributed middle would re- 
sult. 



94 ESSENTIALS OF LOGIC 

PRACTICE ON SECTIONS 19 to 22 

The following examples should be supplemented 
by others, selected from various sources, by the in- 
structor, and especially by the class from their own 
studies, and used for further practice as follows: 
1st. Put each in strict logical form with three terms 
and three propositions, any missing propositions being 
supplied. 2nd. Point out the minor, the major, the 
middle term in that order. 3rd. Indicate the major 
premise, the minor premise, the conclusion. 4th. 
Are both premises negative? If so, what follows? 
5th. Is the middle term total at least once? 6th. Is 
any term total in the conclusion? If so, is it also 
total in its premise? If not, what follows? 

As a further exercise, the class should be required 
to find or invent cases of undistributed middle, illicit 
major, and illicit minor and to bring examples of the 
three kinds of enthymemes. 

In case any example contains parts of two or more 
syllogisms, each one should be fully expressed, and 
tested as above. See especially Section 22. 

1. Some wars being justifiable, while all are inex- 
pedient, it is easy to see that not all inexpedient 
acts are unjustifiable. 

2. Since caterpillars have two legs, while worms do 
not, they cannot be worms. 

3. This man, unlike a thief, shares his money with 
the poor. 

4. All men are sinners and yet some of them are not 

cruel 



MEDIATE DEDUCTION 95 

5. He must be an atheist, for he holds these opinions 

that are held by all atheists. 

6. All who were pledged voted for him, but as Jones 

was not pledged, it follows that he did not. 

7. No science is perfect, but every science ought to 
be cultivated, and so the things we ought to cul- 
tivate are imperfect. 

8. No one is rich who is not content, so of course 
no miser is rich, for he could not possibly be con- 
tent. 

9. All horned animals are ruminants, and so is the 

elk, which is therefore horned. 

10. Every good citizen is ready to defend his coun- 

try, and of course is patriotic, and therefore 
every patriotic man is ready to defend his country. 

11. Few of the passengers could swim, and yet not 

many perished, so that some who were saved 
could not swim. 

12. No plants have the power of locomotion, but the 
lower forms of animal life are of course not 
plants. 

13. There was heavy dew this morning, so it could 

not have been a cloudy night. 

14. Wisdom is the principal thing; therefore get wis- 

dom. Bible. 

15. Keep thy heart with all diligence; for out of it 

are the issues of life. Bible. 

16. How many syllogisms can be made from these ex- 

amples from the Bible? The fear of the Lord is 
the beginning of knowledge. The fear of the 
Lord is to hate evil. The fear of the Lord pro- 



96 ESSENTIALS OF LOGIC 

longeth days. The fear of the Lord is a fountain 
of life. The fear of the Lord, that is wisdom, 
and to depart from evil is understanding. 

17. And Joshua said unto the people: Ye cannot 

serve the Lord: for he is an holy God; he is a 
jealous God; he will not forgive your trans- 
gressions nor your sins. Bible. 

18. And he said to David, Thou art more righteous 
than I : for thou hast rewarded me good, whereas 
I have rewarded thee evil. Bible. 

19. Doth Job fear God for nought? Hast thou not 
made an hedge about him? Bible. 

20. The Lord is my shepherd; I shall not want. 
Bible. 

21. For thy name's sake, O Lord, pardon mine in- 
iquity ; for it is great. Bible. 

22. Fear God, and keep his commandments: for this 
is the whole duty of man. Bible. 

23. Repent ye : for the kingdom of heaven is at hand. 
Bible. 

24. Blessed are the poor in spirit: for theirs is the 
kingdom of heaven. Bible. 

25. John came neither eating nor drinking, and they 

say, He hath a devil. The Son of man came 
eating and drinking, and they say, Behold a man 
gluttonous, and a winebibber, a friend of pub- 
licans and sinners. Bible. 

26. He that is of God heareth God's words : ye there- 
fore hear them not, because ye are not of God. 
Bible. 

27. By the deeds of the law there shall no flesh be 



MEDIATE DEDUCTION 97 

justified in his sight ; for by the law is the knowl- 
edge of sin. Bible. 

28. Being justified by faith, we have peace with God. 
Bible. 

29. Hope that is seen is not hope; for what a man 

seeth, why doth he yet hope for? Bible. 

30. Whom he did foreknow, he also did predestinate 
to be conformed to the image of his Son, that he 
might be the firstborn among many brethren. 
Moreover, whom he did predestinate, them he 
also called; and whom he called, them he also 
justified; and whom he justified, them he also 
glorified. Bible. 

31. For whosoever shall call upon the name of the 
Lord shall be saved. How then shall they call 
on him in whom they have not believed? and 
how shall they believe in him of whom they have 
not heard? and how shall they hear without a 
preacher? And how shall they preach, except 
they be sent? Bible. 

32. Let every soul be subject unto the higher powers. 
For there is no power but of God. Whosoever 
therefore resisteth the power, resisteth the ordi- 
nance of God. Bible. 

33. He that will not apply new remedies must expect 
new evils; for time is the greatest innovator. 
Bacon. 

34. Riches are for spending, and spending for honor 

and good actions; therefore extraordinary ex- 
pense must be limited by the worth of the oc- 
casion. Bacon. 



98 ESSENTIALS OF LOGIC 

35. He must needs be a wise man, he speaks so much 
of himself. Bacon. 

36. Of ambitions, it is less harmful the ambition to 
prevail in great things, than that other to appear 
in everything; for that breeds confusion, and 
mars business. Bacon. 

37. Let not a man trust his victory over his nature too 

far; for nature will be buried a great time, and 
yet revive upon the occasion, or temptation. 
Bacon. 

38. Since there must be borrowing and lending, and 
men are so hard of heart as they will not lend 
freely, usury must be permitted. Bacon. 

39. The discommodities of usury are, first, that it 
makes fewer merchants; for were it not for this 
lazy trade of usury, money would not lie still, 
but would in great part be employed upon mer- 
chandising. Bacon. 

40. It (usury) bringeth the treasure of a realm or state 

into a few hands ; for the usurer being at cer- 
tainties, and others at uncertainties, at the end 
of the game most of the money will be in the 
box. Bacon. 

41. It (usury) beats down the price of land; for the 

employment of money is chiefly either merchan- 
dising, or purchasing, and usury waylays both. 
Bacon. 

42. On the other side, in some other respect usury 
advanceth merchandising; for it is certain that 
the greatest part of trade is driven by young 
merchants upon borrowing at interest. Bacon. 



MEDIATE DEDUCTION 99 

43. Men had need beware how they be too perfect 
in compliments ; for be they never so sufficient 
otherwise, their enviers will be sure to give them 
that attribute, to the disadvantage of their greater 
virtues. Bacon. 

44. I grant that men, continuing what they are, 
Fierce, avaricious, proud, there must be war. 

Cow per. 

45. Why has not man a microscopic eye? 

For the plain reason, man is not a fly. Pope. 

46. Wisdom is a most beautiful thing, and Love is 
of the beautiful ; and therefore Love is also a 
philosopher or lover of wisdom, and being a lover 
of wisdom is in a mean between the wise and 
the ignorant. Plato. 

47. To overcome is pleasant, not to the ambitious 

only, but even to all ; for there arises an imagina- 
tion of superiority, for which all, either in a 
faint or more violent degree, have an appetite. 
But since to overcome is pleasant, it must follow, 
of course, that amusements where there is field 
for rivalry, as those of music and disputations, 
are pleasant ; for it frequently occurs, in the 
course of these, that we overcome. Aristotle. 

48. Happiness does not consist in amusement; for it 
is absurd that the end should be amusement. 
Aristotle. 

49. To amuse ourselves in order that we may be seri- 

ous seems to be right; for amusement resembles 
relaxation. Aristotle. 

50. He is free who lives as he likes ; who is not sub- 3 



ioo ESSENTIALS OF LOGIC 

ject to compulsion, to restraint, or to violence; 
whose pursuits are unhindered, his desires suc- 
cessful, his aversions unincurred. Who, then, 
would wish to lead a wrong course of life? No 
one. No wicked man, then, lives as he likes; 
therefore no such man is free. Epictetus. 

51. Since, then, neither they who are called kings nor 
the friends of kings live as they like, who, then, 
after all, is free? Epictetus. 

52. To whatever objects a person devotes his atten- 

tion, these objects he probably loves. Do men 
ever devote their attention then to (what they 
think) evils? By no means. Or even to things 
indifferent ? No, nor this. It remains, then, that 
good must be the sole object of their attention; 
and if of their attention, of their love too. Who- 
ever, therefore, understands good, is capable like- 
wise of love ; and he who cannot distinguish good 
from evil, and things indifferent from both, how 
is it possible that he can love? The wise per- 
son alone, then, is capable of loving. Epictetus. 

53. You will act in the wisest way, if you deem his 

piety, virtue, and industry to be your own, to be 
with you, wherever you are ; for those things 
which we hold in mind are no less ours than those 
we behold with our eyes. Cicero. 

54. We ought to watch and avoid the love of money; 

for nothing so truly characterizes a narrow, 
groveling disposition as to love riches. Cicero. 

55. An inordinate passion for glory is likewise to be 
guarded against; for it deprives us of liberty, 



MEDIATE DEDUCTION ioi 

the only prize for which men of elevated senti- 
ments ought to contend. Cicero. 

56. But, since most persons are of opinion that the 
achievements of war are more glorious than civil 
affairs, this judgment needs to be restricted; for 
many, as generally is the case with high minds 
and enterprising spirits, especially if they are 
adapted to military life and are fond of warlike 
achievements, have often sought opportunities of 
war from their fondness for glory; but if we 
are willing to judge truly, many are the civil 
employments of greater importance, and of more 
renown, than the military. Cicero. 

57. In this respect friendship is superior to relation- 

ship, because from relationship benevolence can 
be withdrawn and from friendship it cannot ; for 
with the withdrawal of benevolence the very name 
of friendship is done away, while that of rela- 
tionship remains. Cicero. 

58. Because nature can never change, therefore true 

friendships are eternal. Cicero. 

59. He (Scipio) indeed used to say that nothing was 
more difficult than that friendship should con- 
tinue to the end of life; for it often happened 
either that the same course was not expedient 
to both parties or that they held different views 
of politics. Cicero. 

60. When going into exile, he (Tarquin) found out 

whom he had as faithful friends, and whom un- 
faithful ones, since then he could no longer show 
gratitude to either party. Cicero. 



io2 ESSENTIALS OF LOGIC 

61. The reason why cruelty is the most hateful of all 
vices is that it goes first beyond ordinary limits, 
and then beyond those of humanity; that it de- 
vises new kinds of punishments, calls ingenuity 
to aid it in inventing devices for varying and 
lengthening men's torture, and takes delight in 
their sufferings. Seneca. 

62. An anonymous information was laid before me, 

containing a charge against several persons, who 
upon examination denied they were Christians, or 
had ever been so. They repeated after me an 
invocation to the gods, and offered religious rites 
with wine and incense before your statue (which 
for that purpose I had ordered to be brought, 
together with those of the gods), and even re- 
viled the name of Christ: whereas there is no 
forcing, it is said, those who are really Christians 
into any of these compliances : I thought it 
proper, therefore, to discharge them. Pliny. 

63. Anonymous informations ought not to be re- 

ceived in any sort of prosecution. It is intro- 
ducing a very dangerous precedent, and is quite 
foreign to the spirit of our age. Trajan's reply 
to Pliny. 

64. There needed no licensing of books among them 

(the Spartans), for they disliked all but their 
own laconic apothegms, and took a slight occasion 
to chase Archilochus out of the city, perhaps for 
composing in a higher strain than their own sol- 
dierly ballads and roundels could reach to. Mil- 
ton. 



MEDIATE DEDUCTION 103 

65. Where there is much desire to learn, there of 

necessity will be much arguing, much writing, 
many opinions: for opinion in good men is but 
knowledge in the making. Milton. 

66. There is scarce any profession in the common- 
wealth more necessary, which is so slightly per- 
formed. The reasons whereof I conceive to be 
these: First, young scholars make this calling 
their refuge; yea, perchance, before they have 
taken any degree in the university, commence 
schoolmasters in the country, as if nothing else 
were required to set up this profession but only 
a rod and a ferula. Secondly, others who are 
able, use it only as a passage to better prefer- 
ment to patch the rents in their present fortune, 
till they can provide a new one, and betake them- 
selves to some more gainful calling. Thirdly, 
they are disheartened from doing their best with 
the miserable reward which in some places they 
receive, being masters to their children and slaves 
to their parents. Fourthly, being grown rich, 
they grow negligent, and scorn to touch the 
school but by the proxy of the usher. Fuller. 

6y. Hard, rugged, and dull natures of youth acquit 
themselves afterwards the jewels of the country, 
and therefore their dullness at first is to be borne 
with, if they be diligent. Fuller. 

68. The reason that there is such a general outcry 

among us against flatterers is that there are so 
very few good ones. Steele. 

69. The man of business despises the man of pleasure 



104 ESSENTIALS OF LOGIC 

for squandering his time away ; the man of pleas- 
ure pities or laughs at the man of business for 
the same thing ; and yet both concur superciliously 
and absurdly to find fault with the Supreme 
Being for having given them so little time. 
Bolingbroke. 

jo. There never can be wanting some who distinguish 
desert, who will consider that no dictionary of 
a living tongue can ever be perfect, since, while 
it is hastening to publication, some words are 
budding and some falling away. Johnson. 

71. Foolish men imagine that because judgment for 
an evil thing is delayed, there is no justice, but 
an accidental one, here below. Carlyle. 

J2. What, then, is the use of history, and what are 
its lessons? If it can tell us little of the past, 
and nothing of the future, why waste our time 
over so barren a study? 

First, it is a voice ever sounding across the cen- 
turies the laws of right and wrong. Opinions 
alter, manners change, creeds rise and fall, but 
the moral law is written on the tablets of eter- 
nity. For every false word or unrighteous deed, 
for cruelty and oppression, for lust or vanity, the 
price has to be paid at last, not always by the 
chief offenders, but paid by some one. Justice 
and truth alone endure and live. Injustice and 
falsehood may be long-lived, but doomsday comes 
at last to them, in French revolutions and other 
terrible ways. 

That is one lesson of history. Another is, that we 



MEDIATE DEDUCTION 105 

should draw no horoscope; that we should ex- 
pect little, for what we expect will not come to 
pass. Revolutions, reformations, — those vast 
movements into which heroes and saints have flung 
themselves, in the belief that they were the dawn 
of the millennium, — have not borne the fruit 
which they looked for. Froude. 

73. Few things are needed to make a wise man happy ; 
nothing can make a fool content; that is why 
most men are miserable. Rochefoucauld. 

74. Thou art not thyself: 

For thou exist'st on many a thousand grains 
That issue out of dust. Shakespeare. 

23. Conditional Propositions. — Conditional 
propositions are of two kinds, hypothetical and dis- 
junctive. They assert, not absolutely, as do cate- 
gorical propositions (Section 14), but dependently 
on some supposition or alternative. Let us analyze 
some examples. 

First, the hypothetical proposition : 

a. With the same subject in the two clauses: 
if iron be impure, it is brittle; or if iron be a metal, 
it has luster. The first example is equivalent to 
the simple proposition, impure iron is brittle; the 
second is an enthymeme with the major premise " in 
the mind," and the minor stated, not as a fact, but 
as a supposition, thus: (metals have luster), if iron 
be a metal, then iron has luster. 

b. With the subject of the first clause as predi- 



lo6 ESSENTIALS OF LOGIC 

cate of the second: if metals have luster, carbon is 
not a metal. This is an enthymeme with the minor 
premise " in the mind," and the major stated as a 
supposition, thus: if metals have luster (carbon 
has not luster), therefore carbon is not a metal. 
In this form the second clause must be negative, 
else undistributed middle; as if it were said: if met- 
als have luster, iron is a metal (iron having lus- 
ter). 

c. With the predicate of the first clause as sub- 
ject of the second: if iron be a metal, some metals 
are hard; the full syllogism being: (iron is hard), 
and if iron be a metal, some metal is hard. In this 
form the second clause must be partial, else illicit 
minor. 

d. With the same predicate in the two clauses : 
if metals have luster, iron has luster; an enthymeme 
yielding: if metals have luster, (iron is a metal), 
therefore iron has luster. 

e. With different terms for subjects and predi- 
cates of both clauses : if the temperate are constant, 
the prudent are unperturbed, yields the sorites : 
(the prudent are temperate), and if the temperate 
are constant, and (the constant are unperturbed) 
therefore the prudent are unperturbed. 

f. With only two terms as subject and predicate 
of both clauses. Such propositions express all the 
forms of immediate inference allowed by Section 
17, as: 



MEDIATE DEDUCTION 107 

(1) Combination: if a house be a building, a 
brick house is a brick building. 

(2) Contradiction: if animals are mortal, ani- 
mals are not immortal. 

(3) Conversion in all legitimate forms, as: if 
no misers are happy men, no happy men are misers, 
etc. 

(4) Relation of propositions: if all grass be 
green, some grass is green, etc. 

It appears, therefore, that the hypothetical propo- 
sition is equivalent to a simple proposition, or is an 
immediate inference, or is an enthymeme subject to 
the rules of the syllogism. 

Second, the disjunctive proposition: as, for ex- 
ample : actions are either right or wrong, evidently 
a direct application of the primary laws of Sections 
9, 10, and 11 : of two contradictories, one must be 
true, the other false. If the division be not dichot- 
omous, the disjunction is still correct, provided the 
resulting parts exhaust the notion divided, and do 
not overlap, as : angles are right, acute, or obtuse. 
Strict logical form would require contradictories : 
angles are either right or oblique. We speak 
loosely, however, in ordinary interchange of 
thought, or we limit possible affirmation to two op- 
posites not strict contradictories by assuming or 
asking that it be granted that any third possibility 
be not allowed; as: that tree is a birch or a beech, 
when it might be neither; or a suicide is either de- 



io8 ESSENTIALS OF LOGIC 

merited or cowardly, when he might be both, or, per- 
haps, neither. 

Every disjunctive is equivalent to four hypotheti- 
cals ; actions are either right or wrong, yields the fol- 
lowing: if they are right, they are not wrong; if 
they are not right, they are wrong; if they are 
wrong, the are not right; and if they are not wrong, 
they are right. 

Third, the hypothetical and the disjunctive com- 
bined : 

a. With the same condition, and different con- 
clusions : if A is B, C is D ; or if A is B, E is F. 

b. With different conditions, and the same con- 
clusion: if A is B, C is D ; or if E is F, C is D. 

c. With different conditions, and different con- 
clusions : if A is B, C is D ; or if E is F, G is H. 

Subjects or predicates might be repeated as in 
the simple hypothetical above. Being formed of 
the hypothetical and the disjunctive, no new princi- 
ples are needed to explain the combination. A di- 
vision into more than two classes, co-exclusive, and 
exhaustive would be of the form : either A is B, or 
C is D, or E is F ; this would yield a. combined form : 
if A is not B, C is D ; or if A is not B, E is F; and 
other similar forms. It appears, then, that these 
compound forms originate in non-dichotomous di- 
visions. 



MEDIATE DEDUCTION 109 

PRACTICE ON SECTION 23 

For each conditional proposition in the following: 
1st. Is it hypothetical or disjunctive? 2nd. If hypo- 
thetical, is it an immediate inference, and of what 
kind? 3rd. Or is it an enthymeme? If so, complete 
the syllogisms, and test by the rules of Section 20. 
In case undistributed middle or illicit process be 
found, exchanging the subject and predicate of a 
proposition supplied to complete the syllogism, will 
probably correct the error. 4th. If disjunctive, test 
the disjunction, and give at least some of the re- 
sulting conjunctives. 5th. If a simple proposition, 
state it. 

1. Men leave their riches either to their kindred or 
to the public ; and moderate portions prosper best 
in both. Bacon. 

2. If a man write little, he had need have a great 
memory; if he confer little, he had need have a 
present wit; and if he read little, he need have 
much cunning, to seem to know that he doth not. 
Bacon. 

3. Wherever he goes, there is trouble. 

4. If you love me, tell me so. 

5. If wishes were horses, beggars would ride. 

6. He has gone to his cottage or bungalow. 

7. Neither money nor threats could make him change 
his mind. 

8. Everything pleasant consists either in the percep- 
tion of pleasant objects, or in the remembrance 
of those which have already been, or in the hope 



no ESSENTIALS OF LOGIC 

of such as are yet to be; for men exercise per- 
ception on present, memory on past, and hope on 
future objects. Aristotle. 
9, Unless parents afford their children a fit pattern 
of life, they will leave them an obvious excuse 
to quote against themselves. Aristotle. 

10. If I am wrong in this, that I believe the souls of 
men to be immortal, I willingly delude myself. 
Cicero. 

11. Nothing is more noble and more exalted than to 

despise riches if you have them not, and if you 
have them, to employ them in beneficence and 
liberality. Cicero. 

12. If it were expediency that cemented friendships, 
the same when changed would dissolve them. 
Cicero. 

13. There is no reason why power should do any 

harm, if only it be wielded in accordance with 
the laws of nature. Seneca. 

14. No man, unless he be good, can ever be an orator. 

Quintilian. 

15. The mind cannot be in a condition for pursuing 

the most noble of studies, unless it be entirely 
free from vice. Quintilian. 

16. Virtue is teachable, if it is knowledge; for surely 
knowledge is teachable. 

17. Sorrowful and mishappy is the condition of a 
poor beggar, for if he asks not his meat he dieth 
of hunger, and if he ask he dieth for shame; and 
dire necessity constraineth him to ask. Chau- 
cer, quoting Innocent. 



MEDIATE DEDUCTION in 

18. If we never flattered ourselves the flattery of 
others would not hurt us. Rochefoucauld. 

19. Those many had not dared to do that evil 
If the first man that did the edict infringe 
Had answered for his deed. Shakespeare. 

20. If ye then, being evil, know how to give good 
gifts unto your children, how much more shall 
your Father which is in heaven give good things 
to them that ask Him? Bible. 

21. Had ye believed Moses, ye would have believed 

me; for he wrote of me. But if ye believe not 
his writings, how shall ye believe my words? 
Bible. 

22. If ye believe not that I am he, ye shall die in your 
sins. Bible. 

23. If God were your Father, ye would love me; for 

I proceedeth forth and came from God ; neither 
came I of myself, but he sent me. Bible. 

24. If a man keep my saying, he shall never see death. 
Bible. 

25. Neither hath this man sinned, nor his parents. 
Bible. 

26. If this counsel or this work be of men, it will 
come to nought; but if it be of God, ye cannot 
overthrow it ; lest haply ye be found even to fight 
against God. Bible. 

27. If God be for us, who can be against us? Bible. 

28. If ye were Abraham's seed, ye would do the 
works of Abraham. Bible. 

29. I will not letthee go, unless thou bless me. Bible. 

30. If this which I have mentioned be the meaning of 



ii2 ESSENTIALS OF LOGIC 

the word liberty, in the ordinary use of language : 
as I trust that none that has ever learned to talk, 
and is unprejudiced, will deny: then it will follow 
that in propriety of speech neither liberty, nor its 
contrary, can properly be ascribed to any being or 
thing but that which has such a faculty, power 
or property as is called will. Edwards. 

31. The taxes are indeed very heavy, and, if those 
laid on by the government were the only ones we 
had to pay, we might more easily discharge them ; 
but we have many others, and much more griev- 
ous to some of us. Franklin. 

32. If time be of all things the most precious, wasting 

time must be the greatest prodigality. Franklin. 

33. If you would have a faithful servant, and one that 
you like, serve yourself. Franklin. 

34. If you would know the value of money, go and 

try to borrow some. Franklin. 

35. If a man have no heroism in his soul — no ani- 
mating purpose beyond living easily and faring 
sumptuously — I can imagine no greater mistake 
on his part than that of resorting to authorship as 
a vocation. Greeley. 

36. If the bell rings, why should we run? Thoreau. 

See 9, page 128. 

37. It is worth the expense of youthful days and costly 
hours, if you learn only some words of an an- 
cient language, which are raised out of the 
trivialness of the street, to be perpetual sugges- 
tions and provocation. Thoreau. 

38. When works of importance are pressing, generals 



MEDIATE DEDUCTION 113 

themselves may take up the pickax and the spade. 
Bolingbroke. 

39. No man would have any reason to fear the fury 
of a tyrant, if he had no authority over any but 
from fear ; since, as a single man, his bodily force 
can reach but a small way, and all the further 
power he possesses must be founded either on 
our own opinion, or on the presumed opinion of 
others. Hume. 

40. If we suffer ourselves to imagine that their senses 
present to different men different images of 
things, this skeptical proceeding will make every 
sort of reasoning on every subject vain and friv- 
olous. Burke. 

41. But should any man be found who declares that 
to him tobacco has a taste like sugar, and that 
he cannot distinguish between milk and vinegar; 
or that tobacco and vinegar are sweet, milk bit- 
ter, and sugar sour; we immediately conclude 
that the organs of this man are out of order, 
and that his palate is utterly vitiated. Burke. 

42. Indeed, my lord, I greatly deceive myself, if in 
this hard season (after the loss of his son), I 
would give a peck of refuse wheat for all that 
is called fame and honor in the world. Burke. 

43. If it be admitted that a man possessing absolute 

power may misuse that power by wronging his 
adversaries, why should a majority not be liable 
to the same reproach? De Tocqueville. 

44. When a community actually has a mixed govern- 

ment — that is to say, when it is equally divided 



ii4 ESSENTIALS OF LOGIC 

between two adverse principles — it must either 
pass through a revolution or fall into complete 
dissolution. De Tocqueville. 

45. When an individual or party is wronged in the 

United States, to whom can he apply for redress ? 
If to public opinion, public opinion constitutes 
the majority; if to the legislature, it represents 
the majority, and implicitly obeys its instructions; 
if to the executive power, it is appointed by the 
majority, and is a passive tool in its hands. The 
public troops consist of the majority under arms; 
the jury is the majority invested with the right 
of hearing judicial cases; and in certain cases, 
even the judges are elected by the majority. 
However iniquitous or absurd the evil of which 
you complain may be, you must submit to it as 
well as you can. 
If, on the other hand, a legislative power could be so 
constituted as to represent the majority without 
necessarily being the slave of its passions, an 
executive so as to retain a certain degree of un- 
controlled authority, and a judiciary so as to re- 
main independent of the other two powers, a 
government would be formed which would still 
be democratic, without incurring any risk of 
tyranny. De Tocqueville. 

46. On a hot sunshiny afternoon came on a sudden 

storm and spoiled the farmer's hay; and this is 
called ill luck. We will suppose the same event 
to take place when meteorology shall have been 
perfected into a science, provided with unerring 



MEDIATE DEDUCTION 115 

instruments; but which the farmer had neglected 
to examine. This is no longer ill luck, but im- 
prudence. Coleridge. 

47. Take away Stonehenge from Salisbury Plain, and 

it is nothing more than Hounslow Heath, or 
any other uninclosed down. Byron. 

48. It cannot be true: if Alexander were dead, the 
whole habitable world would have smelt of his 
carcass. Demades, quoted by Grote. 

24. So-Called Conditional " Syllogisms." — 

Examples are as follows: 

First, based on hypothetical propositions : if A 
is B, C is D; but A is B, therefore C is D: or, but 
C is not D, therefore A is not B. 

Second, based on disjunctive propositions: A is 
either B or non-B ; but A is B, therefore A is not 
non-B, etc. 

Third, based on the combined form: Either if 
A is B, C is D ; or if E is F, G is H ; but either A 
is B, or E is F ; therefore C is D, or G is H : or, but 
either C is not D, or G is not H ; therefore A is not 
B, or E is not F. 

We have seen in Section 23 that the hypothetical 
proposition is itself an incomplete syllogism; fur- 
thermore, the above forms have more than three 
terms, have not major and minor premises as de- 
fined for the syllogism in Section 19, in which a 
major and a minor term are compared respectively 
with a middle term. These forms are therefore not 



n6 ESSENTIALS OF LOGIC 

syllogisms, and the question arises what is their true 
nature and their place in logic. Examination of 
them will show that each constitutes a passage from 
a supposition or an alternation, that is from a state- 
ment of mere dependence, or connection, to an inde- 
pendent statement of exactly the same subject-mat- 
ter. In the original proposition, if hypothetical, it is 
affirmed merely that the conclusion follows from the 
condition, and the question of the truth of the con- 
dition or conclusion is not involved; in the second 
proposition either the truth of the condition or the 
falsity of the conclusion is affirmed, and conclusion 
is reached as to the truth of the other clause. Again, 
if the original proposition be disjunctive, it is af- 
firmed merely that one or the other of two contra- 
dictories is true, the other false; but not which is 
true, and which false; in the second proposition 
the truth or the falsity of one alternative is af- 
firmed, and the falsity of the truth of the other 
concluded. This is evidently not an instance of 
syllogistic reasoning. 

Since logic deals with sequence, not with truth, 
these forms of expression, convenient and frequent 
as they are, are outside of its proper territory, and 
are evidently not forms of reasoning, all the reason- 
ing in them being confined to the original proposi- 
tion, in itself a syllogism. For dealing with these 
forms, however, it is convenient to express the fact 
that in a correct syllogism true premises yield a 



MEDIATE DEDUCTION 117 

true conclusion, and a false conclusion means a 
false premise, in the following rules: 

(1) Affirming the antecedent affirms the con- 
sequent. 

(2) Denying the consequent denies the ante- 
cedent. 

It will be seen that these rules cover the so- 
called hypothetical syllogism, while for disjunctive 
forms the laws of contradiction and exclusion apply 
directly. 

25. Mathematical Syllogisms. — Mathemati- 
cal syllogisms are those whose premises are mathe- 
matical propositions (Section 15, end). Just as 
the methods and rules for immediate inference were 
seen in Section 17 a to be simplified when applied 
to the mathematical proposition, so it is with the 
mathematical syllogism. All terms being total, and 
equivalent in their quantity, there is no distinction 
between major and minor term, or therefore be- 
tween major and minor premise; no possibility of 
" undistributed middle," or of " illicit process," be- 
cause these errors depend upon the partial use of 
a term. Figure and mood (see Appendix, page 
118) have no significance. 

The rules of the mathematical syllogism reduce 
to the simple forms : two quantities equal to a third, 
are equal to each other; and a quantity greater (or 
less) than another which is greater (or less) 
than a third, is still greater (or less) than the 



n8 ESSENTIALS OF LOGIC 

third quantity. The mathematical forms of the 
copula are: " is equal to," " is unequal to," the lat- 
ter resolving into the two forms : " is greater than," 
and " is less than." Many expressions such as : 
" is part of," ■ - is included in," " contains," " is one 
of," " is above," " is below," or any comparative 
degree, are combinations of the mathematical copula 
with other elements, and may easily be put in strict 
form: John is taller than James, George is taller 
than John, therefore George is taller than James, 
would become: the height of John is greater than 
that of James, etc. 

APPENDIX TO CHAPTER VI 
Figure and Mood. — As the middle term of a 
syllogism may be either the subject or the predicate 
of the major and of the minor premise, it is evident 
that there are four possible combinations of the po- 
sition of the middle term in the two premises, de- 
termining what are called the " figures " of the syllo- 
gism. In the first figure, the middle term is sub- 
ject of the major premise and predicate of the 
minor; in the second figure, it is predicate of both 
premises; in the third, subject of both; and in the 
fourth, predicate of the major and subject of the 
minor premise. 

Granted the rules of the syllogism in Section 20, 
it follows that in figure 1 the major premise must 
be total and the minor affirmative; in figure 2, the 



MEDIATE DEDUCTION 119 

major must be total and one premise negative; in 
figure 3, the minor premise must be affirmative and 
the conclusion partial. The proof of these special 
rules affords a valuable exercise for the student. It 
is important to note in this connection that the only 
positions in which a term is thought of totally are 
the subject of A or E, and the predicate of E or O. 
The fourth figure is open to criticism, and need not 
be discussed here. 

It is further evident that the major and minor 
premises in any figure may be various combinations 
of A, E, I, and O, the conclusion being of course 
determined by the premises. Sixteen such combina- 
tions, called " moods " of the syllogism, are possi- 
ble: AA, AE, AI, AO, EA, EE, EI, EO, IA, IE, 
II, IO, OA, OE, 01, 00. It can be shown that 
EE, EO, IE, II, 10, OE, 01, 00, as premises, 
would violate the rules in Section 20, the proof of 
which can be used as an exercise. The only valid 
combinations, then, are AA, AE, AI, AO, EA, EI, 
IA, OA. 

As a further exercise it can be proved from the 
rules in Section 20 or from the special rules above, 
that some of these eight moods are not valid in 
some of the four figures, leaving only the following: 
AA in figures 1, 3, and (4) ; AE in 2, (4) ; AI in 
1, 3; AO in 2; EA in 1, 2, 3, (4) ; EI in 1, 2, 3, 
(4) ; IA in 3, (4) ; OA in 3. These nineteen possi- 
ble moods have been named, the vowels in the name 



120 ESSENTIALS OF LOGIC 

of each being the symbols of its three propositions, 
and the names of the moods in each figure are 
grouped together in the following mnemonic hexa- 
meters : 

BARBARA, CELARENT, DARK, FERIOque 
prioris : 

CESARE, CAMESTRES, FESTINO, FA- 
KOFO, secundae; 

Tertia, DARAPTI, DISAMIS, DATISI, FE- 
LAPTON, 

DOKAMOK,* FERISON habet. Quarta in- 
super addit 

BRAMANTIP, CAMENES, DIMARIS, FE- 
SAPO, FRESISON. 

In these names the initial consonant is the same 
as that of the mood (Barbara, Celarent, Darii, or 
Ferio) in Figure i, to which the moods in the other 
figures may be changed by following the directions 
indicated by these other consonants in their names 
(for processes, see Section 17) : 

" s " means, convert simply the proposition 
whose symbol precedes the " s " ; " p," convert by 
limitation the preceding proposition ; " f," infer by 
contradiction; "k," apply " f," and then " s " to 
the preceding proposition ; " m," exchange the prem- 
ises. 

The other consonants in the names have no mean- 
ing. For practice, any syllogism not in the first 
*0r Fokmafokf. 



MEDIATE DEDUCTION 121 

figure may be used, e. g., Some wars are justifiable, 
all wars are inexpedient, and so some inexpedient 
acts are justifiable, is Disamis, which becomes Darii, 
as follows: All wars are inexpedient, some justi- 
fiable acts are wars, and so some justifiable acts are 
inexpedient. 



CHAPTER VII 

DEDUCTIVE FALLACIES 

26. The Nature of Fallacy. — Any violation 
of the laws, principles, or rules of logic is a fallacy. 
The only reason for separate consideration of the 
subject here is that these errors may be brought to- 
gether and classified, and their causes, some of which 
lie outside of logical forms, examined. It must be 
remembered that there are many false statements 
which are not fallacies, that fallacy is not all, but 
only part of error. 

A fallacy, therefore, is a violation of one of the 
following : 

(1) The rules of division in Section yb; (2) 
the rules of definition in Section yc; (3) the laws 
of affirmation, denial, or exclusion in Sections 9, 
10, 11 ; (4) the limits of immediate inference in Sec- 
tion 17; (5) the rules of the syllogism in Section 
20; (6) the right to clear expression of the thought. 

If therefore we apply correctly these rules, we 
can detect fallacy. There are, however, some more 
or less obscure causes of such violation of logical 
law, that it is helpful to examine closely. The chief 

122 



DEDUCTIVE FALLACIES 123 

of these are found in the Sections 2.7 and 28 follow- 
ing. 

27. Ambiguity. — The fallacy consists in 
taking the wrong meaning, or in case of a syllogism, 
in using first one, then the other meaning, which 
gives four terms. There are two general cases. 

First, an ambiguous term. 

(1) The term has two meanings, as in: clubs 
are organized groups of persons, some weapons are 
clubs, therefore some weapons are organized groups 
of persons ; or, all criminal actions ought to be pun- 
ished, prosecution for theft is a criminal action, and 
ought to be punished ; or again, a fox is a quadruped, 
Herod is a fox, therefore a quadruped. 

To the countless ambiguities of language are due 
the frequent instances of this fallacy. Here, too, 
belongs the duplicity of the pun. 

(2) The term is used once collectively, once dis- 
tributively, as : two and three are even and odd, two 
and three are five, therefore five is even and odd. 

(3) The wrong accent or tone causes ambigu- 
ity: A asked the officer to arrest B, and the offi- 
cer arrested him, or him. 

(4) The term is once limited in some way, once 
not, as : relieving pain is right, killing a sufferer re- 
lieves his pain, therefore killing a sufferer is right. 

Second, an ambiguous sentence, the fallacy being 
to take the wrong sense. 

( 1 ) The sentence has an ambiguous grammati- 



i2 4 ESSENTIALS OF LOGIC 

cal structure, as: I predict the enemy our troops 
will defeat; Moses was the daughter of Pharaoh's 
son; in athletics only he excelled; I will go and re- 
turn next week; lost, an umbrella by a gentleman 
with a carved head. 

(2) The wrong accent may change the meaning 
of the sentence, as above of a term; thus, the sen- 
tence: no man is very fond of receiving useless 
gifts, might be given five different meanings by em- 
phasizing in turn each of the underscored words. 

(3) Incorrect punctuation may cause this fal- 
lacy, as : there were very few occupants who were 
not injured; and, there were very few occupants, 
who were not injured. 

28. Misproof. — Correct proof proceeds from 
premise to conclusion, according to the laws of logic. 
If a premise be questioned, or questionable, it must 
be shown to follow as a conclusion from unques- 
tioned prior premises and these from others, and 
so on, which means that the ultimate ground of 
proof is found in the facts of consciousness given 
to intellect or to sense. These, being self-evident 
or established by scientific induction, are the sure 
foundation for all deduced conclusions. Inductive 
proof is considered in Part III. 

But suppose we desire to prove a proposition false, 
as in debate. Reference to the relation of proposi- 
tions in Section 17 will show that A is overthrown 
by its contradictory, O, and E by I. It is easier to 



DEDUCTIVE FALLACIES 125 

overthrow a total proposition, and to prove a par- 
tial proposition. 

(1) Misproof occurs when some other than the 
proposition stated is proved. This may occur from 
confusion, or may be intentional, as in attacking the 
character of an opponent (argumentum ad ho- 
minem) ; appealing to the prejudice (ad populum) ; 
or to authority without evidence of validity (ad 
verecundiam). 

(2) When we attempt to overthrow a proposi- 
tion by any other than its contradictory. The fal- 
lacy may be disguised by lengthy development of 
the proof, or by some of the many forms of am- 
biguity. 

(3) Here may be mentioned the fallacy of in- 
ferring the falsity of the conclusion from the falsity 
of a premise, or the truth of a premise from the 
truth of the conclusion ; especially in the form of the 
so-called conditional syllogisms when the rules of 
Section 24 are reversed and it is inferred that de- 
nying the antecedent denies the consequent or 
affirming the consequent affirms the antecedent. 

(4) " Begging the question " has many varie- 
ties, all of which include, however, the assumption 
of some essential part of what is sought to be 
proved. In other words, no premise may be used 
without its truth being conceded or proven. 

a. The assumption of the desired conclusion, or 
of a premise which is afterward proved by the very 



126 ESSENTIALS OF LOGIC 

conclusion it is supposed to establish. The final 
conclusion is used as a premise in the course of the 
argument, and the longer and more involved the 
reasoning, the more difficult is it to detect the fal- 
lacy. Plato in one of his writings seeks to prove 
the immortality of the soul from its simplicity; in 
another, its simplicity from its immortality. If we 
say, glass is easily broken, because it is brittle, we 
commit the fallacy. 

b. The assumption of a universal premise in or- 
der to prove a particular conclusion, as : this man is 
a sinner, because all who suffer are sinners and he 
is suffering. 

c. To assume the particular and from it to argue 
the universal, is both begging the question and il- 
licit process ; if all the parts are assumed one by one, 
it is begging the question only. 

d. The assumption that implication, as in Sec- 
tion 1 6, is proof. 

e. The demand of a yes or no answer to a com- 
pound question ; as : are you good and stupid ? is he 
wicked and foolish? have I the wrong pig by the 
ear? 

/. The assumption of unproven facts in a ques- 
tion ; as : have you ceased to steal chickens ? why is 
a politician always a hypocrite? An imperfect dis- 
junction is of this nature, as: either you have 
ceased to steal chickens, or you are still stealing 
them. If, however, the third possibility, the ex- 



DEDUCTIVE FALLACIES 127 

istence of which renders the disjunction imperfect, 
be shown or be granted false, no fallacy is involved. 
In this case the third possibility is : you have not 
been a chicken thief. And a politician may not 
always be a hypocrite. 

PRACTICE ON SECTIONS 26 to 28 
The more obvious fallacies have already been exem- 
plified under the various heads of definition, division, 
inference, etc. Examine the following examples, and 
point out what fallacy, if any, is present; classify 
each fallacy according to the subdivisions of Sections 
26, 2J, and 28; and, if possible, show how it may be 
avoided. 

1. Since God is Infinite, it follows that the Infinite 
is God. 

2. If John is the uncle of James, and Mary is John's 
sister, then it follows that James is Mary's 
nephew. 

3. Penny wise, pound foolish. 

4. As all animal life comes from eggs, it follows that 

all eggs are the product of some animal. 

5. The duke yet lives that Henry shall depose, 
And him outlive, and die a violent death. Shake- 
speare. 

6. Scott's works were read not only by his country- 
men, but by all educated people in Europe. 

7. "Where's your father, boy?" "He's down at 
the other end of the field with the hogs. You 
can tell him by his hat." 

8. " Young ladies, here is your new teacher, Mr. 



128 ESSENTIALS OF LOGIC 

Chase. Tell him what your other teacher did 
first, so he can go on in the same way." " She 
kissed us." 
9. " Ring the door-bell, Mister, I can't reach it." 
" Thank you, sir. Now run." 

10. If I can have the luxuries of life, I can do with- 

out the necessities. 

11. If you never succeed in anything you undertake, 
you can never undertake anything in which you 
will succeed. 

12. Some possible cases are improbable, therefore 
some probable cases are impossible. 

13. He has little natural ability and still less educa- 
tion. 

14. He is the very man, of all others, whom I despise 
most. 

15. The secretary and treasurer of the company was 

both the secretary and the treasurer. 

16. Saddle me the ass; and they saddled him. 

17. " You called me a sneak." "Yes, it is true, and 

I am sorry." 

18. Examine carefully the two next examples, or the 

next two examples. 

19. "Do you know the men on the jury?" "Yes, 
more than half of them." " Are you willing to 
swear to that ? " " Yes, I know more than all 
of them." 

20. If Croesus should wage war against the Persians, 

he would destroy a mighty empire. 

21. What is seen is visible, what is heard is audible, 

therefore what is desired is desirable. 

22. All the angles, A, B, and C, of a triangle, are 



DEDUCTIVE FALLACIES 129 

less than two right angles; therefore A is less 
than two right angles. 

23. All the angles of a triangle are equal to two right 

angles; therefore A is equal to two right angles. 

24. Heat expands bodies, therefore cold contracts 
them. 

25. Beefsteak is wholesome food, and therefore good 

for fever patients. 

26. Gambling is wrong because it is opposed to sound 
ethical principles. 

27. The length of the day for labor ought not to be 
fixed by law, for all legislation that interferes 
with right of free contract is bad. 

28. Why does not the King of England wish to be 
buried in a Catholic graveyard? 

29. Men of severe climates are hardy, therefore such 
a climate is desirable. 

30. If he did not steal the stuff, why did he hide it so 

carefully ? 

31. I will not have a doctor; all who have died of this 

disease have had doctors. 

32. Advice is useless for you must advise a man what 
he will do or what he will not do. 

33. Great minds run in the same channel. 

34. Great men have been derided, just as I am now 
being derided. 

35. Iron is becoming rarer, for it is a useful metal, 
and they are becoming rarer. 

36. Epimenides the Cretan says that all the Cretans 

are liars, and being a Cretan, he is a liar; but 
being a liar, the Cretans are not liars, because this 
liar says they are liars; therefore, being a Crs- 



130 ESSENTIALS OF LOGIC 

tan, he is not a liar, and so on, as the surveyors 
say, to the beginning. 

37. In the meanwhile, the method I have observed 
toward those who have been brought before me 
as Christians is this : I asked them whether they 
were Christians; if they admitted it, I repeated 
the question twice, and threatened them with pun- 
ishment ; if they persisted, I ordered them at 
once to be punished; for I was persuaded what- 
ever the nature of their opinions might be, a 
contumacious and inflexible obstinacy certainly 
deserved correction. Pliny. 

38. We have computed the inhabitants and contem- 

plated the public works of the Roman Empire. 
The observation of the number and greatness of 
its cities will serve to confirm the former and 
multiply the latter. Gibbon. 

39. For sale, an assorted lot of red men's socks. 

40. The place contains some two or three hundred 

houses and twenty-five hundred inhabitants, all 
standing with their gable ends to the street. 

41. If a wife be beautiful, she excites jealousy; if 

she be ugly, she excites disgust; therefore it is 
best not to marry. 

42. Governments ought to be resisted, for they repress 

the liberties of mankind. 

43. All persons are hereby forbidden to ride or drive 

cattle through this park. 

44. L T pon which the Moor, seizing a bolster full of 

rage and jealousy, smothered the unhappy Des- 
demona. 



DEDUCTIVE FALLACIES 131 

45. Erected to the memory of John Phillips, acci- 

dentally shot as a mark of affection by his 
brother. 

46. If some people are wise, then, of course, some 
are foolish. 

47. An agnostic believes that nothing can be certainly 
known. 

48. Protagoras taught Euathlus law. Euathlus 
agreed to pay his tuition when he won his first 
case. He had no case, and Protagoras sued him, 
saying, If the judgment of the court be against 
you, it will give me the fee ; if in your favor, you 
will owe me the fee, for you will have won your 
first case. 

Euathlus replied : "If the decree be in my favor, 
I need not pay; if adverse, I shall have lost my 
first case, and shall owe you nothing." 

49. Let us compel every able-bodied male member of 

the community, who is nineteen years of age, 
and not absolutely indispensable at home, to vol- 
unteer as a member of this military company. 

50. What should be done with a man who marries 

his deceased widow's sister? 

51. Human thought is bounded only by the infinite. 

52. Does one grain of corn make a heap? No? Do 
two? Three? Etc. 

53. If you pull one hair from a man's head, will it 
make him bald? Will two? Three? Etc. 

54. Every object that does not decompose white light, 

is seen by white light, and therefore white; a 
black object does not, and is white. 



132 ESSENTIALS OF LOGIC 

55. Conscience is something within that tells me when 
I have done wrong ; I had it once, and they had to 
send for the doctor. 

56. Nuisances are punishable by law; a noisy dog is 
a nuisance. 

57. Time is either past or future; the past is gone, 
the future has not come; there is no time. 

58. Whoever necessarily goes or stays is not a free 

agent; but every one necessarily goes or stays, 
and so no one is free. 

59. I love to steal — I love to steal — I love to steal 
a while away. 

60. To pray for rain is to ask for a miracle; but 
miracles have ceased. But, prayer for rain has 
often been followed by rain; and men have suc- 
ceeded in causing rain, and it is therefore impious 
to suppose God cannot. 

61. Prayer is useful if it informs God of what He 
does not know, or if it effects a change in his 
purposes ; but prayer can do neither, and is there- 
fore useless. 

62. Winning a large prize in a lottery is not an un- 

common occurrence, and may therefore reason- 
ably be expected. 

63. He that is of God heareth the words of God; 
for this cause ye hear them not, because ye are 
not of God. Bible. 

64. Everything of which there is an innate appetite 

is pleasant; for appetite is a desire of what is 
pleasant. 

65. No man should choose young people to be cap- 



DEDUCTIVE FALLACIES 133 

tains and governors, forasmuch as there is no 
certainty in their wisdom. Alexander of Mace- 
don vanquished and conquered Egypt, Judea, 
Chaldee, Africa, and Assyria unto the marches 
of Bargmans more by the counsel of old men 
than by the strength of the young men. Caxton. 

66. The heavier the fall of snow, the better, for it 
provides the poor with more work in cleaning 
it off. 

67. " Step over and see how old Mrs. Jernigan is 
this morning." Later. " She says she was 
forty-nine her last birthday, and please, ma'am, 
why did you want to know ? " 

68. Instead of purity resulting from that arrange- 
ment to India, England herself would soon be 
tainted. Macaulay. 

69. In one evening I counted twenty-seven meteors 
sitting on my back porch. 

70. " Fred got shot to-day." " Where? How? Was 
he hurt much ? " He got shot in a hardware store. 

71. "He's in the quicksand, you say? How far?" 

" Up to his ankles." " Then, there's plenty of 
time." " But he went in head first." 

72. In order to show the relation of the religion of 

Israel to that of heathen nations, Kuenen as- 
sumes : " The Israelitish religion is one of those 
religions; nothing less, but also nothing more." 
J2>- At the outset of his book on " Prophets and 
Prophecy," Kuenen says : " Prophecy is accord- 
ing to this new view, a phenomenon, yet one of 
the most important and remarkable phenomena, 



i 3 4 ESSENTIALS OF LOGIC 

in the history of religion, but just on that ac- 
count a human phenomenon, proceeding from 
Israel, directed to Israel." 

74. So soon as we derive a separate part of Israel's 
religious life directly from God, and allow the 
supernatural or immediate revelation to intervene 
in even one single point, so long also our view 
of the whole continues to be incorrect. Kuenen. 

75. The patriarchs cannot be taken as individuals. 
If individuals Reuben, Gad, and Judah never ex- 
isted, it is plain that individuals Jacob, Esau, and 
Abraham cannot have any more substantial real- 
ity. We have to do here with figures of the 
poetic or legend-building imagination. H. P. 
Smith. 

j6. God, in creating, theomorphises man; man, there- 
fore, necessarily anthropomorphises God. Jacobi. 

yy. Bethel, Hebron, Beersheba, and Shechem were re- 
garded with peculiar veneration by the Israelites. 
Because there were graves at some of these 
places, Stade thinks their sacredness due to an- 
cestor-worship. 

78. A body moves either where it is or where it is 

not, but it cannot move where it is for lack of 
room; nor can it move where it is not, for it is 
not there to move ; therefore a body cannot move. 

79. Since we are forbidden to kill, capital punishment 
is wrong. 

80. A mouse is an animal, and it follows that a large 

mouse is a large animal. 

81. He who is hungriest eats most, and one who eats 



DEDUCTIVE FALLACIES 135 

least is hungriest; therefore he who eats least, 

eats most. 
&2. What I see as the train recedes grows smaller and 

smaller, but as the train does not grow smaller, 

what I see is not the train. 
83. No soldiers but those well qualified should be 

brought on the field; therefore none but veterans 

should be brought on. 



PART III 
INDUCTIVE INFERENCE 



CHAPTER VIII 

THE NATURE AND LAWS OF INDUCTION 

29. Induction and Deduction. — We have seen 
in Part II that by inference immediate or medi- 
ate one proposition may be concluded from one or 
two others as premises; also that these premises 
may themselves be the conclusions of prior infer- 
ence. The question is thus suggested, where is the 
end of this process of referring one proposition to 
another as its higher ground, and that to still an- 
other, and so on; where, in short, is the beginning 
of the chain, where is the original fountain of 
knowledge? 

The sources of knowledge are two, the intellect 
and the senses. Through intellectual discernment 
we know, for example, space, time, causation, moral 
quality, and such truths as : things equal to the same 
thing are equal to each other; two straight lines can- 
not enclose an area ; one of two contradictories can- 
not be affirmed of the other; all personal ac- 
tions are right or wrong; every change has a cause. 
These intellectual truths and the conclusions de- 
rived from them by correct deduction constitute a 
body of certain knowledge. Of this nature are the 

139 



140 ESSENTIALS OF LOGIC 

sciences of mathematics, logic, and ethics, and the 
fundamental principles of all science. 

From the other source of knowledge, the senses, 
comes the knowledge, not of universal, necessary 
truths like those above cited, but only of individual 
facts perceived. From these facts, stated in the form 
of particular propositions, we infer immediately 
universal propositions, thus reasoning from " some," 
often only one, to " all " cases of the kind. This is 
" induction, " already mentioned in Section 16. If, 
for example, we observe that several persons in a 
place we are visiting speak with a peculiar accent, 
we infer that others, perhaps all, speak so; if one 
hot iron burns one finger, we infer that any iron, 
equally hot, will burn any part of the body. 

It is evident that this inference from " some " to 
" all," which as deduction would be the " illicit 
process " of Section 20, must therefore be justified 
by other principles than those justifying deduction. 
These are treated in Sections 31 and 32. 

It is further evident that these inductive universal 
propositions may be used as premises for deduc- 
tions, thus constituting a body of knowledge whose 
truth depends upon the truth of the original induc- 
tive premises. 

30. Scientific Induction. — As was indicated 
above, induction is an immediate inference from a 
particular premise to a universal conclusion ; that is, 
from I to A, or from O to E. The two proposi- 



INDUCTION 141 

tions are either both affirmative or both negative, 
their subjects and their predicates are the same, the 
only change being that the " some " of the premise 
becomes the " all " of the conclusion. The mere in- 
ductive step is seen to be very simple, but its sweep 
takes in the universe, and must be carefully 
guarded. For an inductive conclusion to be true, it 
is necessary that (1) the premise be established by 
correct observation; (2) the conclusion includes 
cases beyond actual observation, else there is no in- 
duction; (3) the step be justified by some authori- 
tative principle. This justification is found in the 
fact and the laws of causation, and we may define 
scientific induction as an immediate inference that 
a particular observed causal connection is uni- 
versal. 

Fuller discussion of causation will be found in 
the next section. The " observation " mentioned 
above means attention to what we see, hear, taste, 
or perceive through any of our senses, including the 
internal sense by means of which the mind per- 
ceives its own states while they are actually pres- 
ent. These " percepts " of the senses are what is 
meant by " experience; " they are often called 
" phenomena." The artificial arrangement of cir- 
cumstances for purposes of observation, is called 
experimenting. This greatly enlarges the scope of 
observation, and furthers causal investigations. 

The essential properties of things that we observe 



142 ESSENTIALS OF LOGIC 

in co-existence, those qualities without which things 
would not be what they are, but something else, 
these are permanent unchanging relations, and form 
the basis for the classifications described in Part I. 
Other co-existing phenomena, and especially succes- 
sive phenomena, we observe also, and it is these 
" accidental " properties, or " changes," that form 
the basis of inductive thought. 

Knowledge of essential, permanent qualities, 
therefore, is the basis of the classification of things 
into systems of genera and species; knowledge of 
their non-essential, changing qualities, is the basis 
of assigning things to their causes. When every 
body occupying space is properly classified in a sys- 
tem of genera and species, and every change occu- 
pying time is explained by reference to its cause, 
natural science will be complete. 

31. Causation. — We know that changes are 
of constant occurrence. What we see, hear, touch, 
etc., is continually changing. We know that these 
changes are not brought about by our effort, we 
know by intellectual discernment that they must 
have a cause, and therefore we know that the law 
that every change has a cause, is not a mere law 
of mind, but is a real fact in the world of things 
external to mind. 

" Every change has a cause." What, then, is a 
cause? Not a mere condition. A body can not 
move except in space and time, both conditions, 



INDUCTION 143 

neither a cause of motion. So the ear is a condi- 
tion of normal hearing, the eye of sight, yet neither 
one is the cause. Without the condition, the thing 
it conditions can not be; given the condition, it still 
may not be. Given the cause, the change must be. 
A condition is negative, in that its absence prevents ; 
a cause is positive, in that its presence compels. 

The cause is that which actually produces the 
change, or event. The cause includes all and only 
those forms and amounts of energy necessary to 
the change; the effect all and only those resulting 
from the change. We look at circumstances, ma- 
terial objects, forces, etc., without analysis, and we 
may select one which interests us, which is added 
last to those already present, or which attracts at- 
tention for any reason, and we call that one the 
cause. But a cause is usually not single or simple; 
many circumstances, antecedents, forces, or what- 
ever name be given them, may contribute to the ef- 
fect, which is likewise complex. We say, a bullet 
killed him, but another by his side may have been 
struck by a bullet, and live. The velocity, the spot 
hit, the condition of health, the strength of the con- 
stitution, the skill of the physician, are all circum- 
stances that may and do enter into the total which 
we may correctly call the cause. Likewise the ef- 
fect summed up as death, may also, when analyzed, 
be seen to include the laceration of certain tissues, 
the rupture of certain blood-vessels, the injury of a 



144 ESSENTIALS OF LOGIC 

nerve, the fracture of a bone; whence is seen the 
complexity of the effect also. 

It is evidently a practical impossibility to state 
all the elements of a cause or an effect ; but we can 
approximate closely enough for reasonable cer- 
tainty. 

32. Uniformity. — Not only has every change 
a cause, but we intuitively know that every like 
change has a like cause, and every like cause has a 
like effect. In other words, causes differing only 
in time and place have effects differing only in time 
and place, and effects differing only so have causes 
differing only so. This principle of " uniformity " 
needs no proof, can have none, is self-evident, and 
universally admitted to be true. 

Because of imperfect observation or other rea- 
sons, we can not always distinguish causes that are 
actually unlike, or effects that are. It often seems 
that the same cause has different effects ; for exam- 
ple, heat melts ice, bakes clay, contracts water, ex- 
pands it, and so on. But the fact that we may not 
see any difference in the causes does not shake our 
belief that they are different; we are certain that 
they are. We speak, however, of such cases as if 
the same cause had unlike effects. We do this also 
in cases where we do distinguish differences in the 
cause. We say, for example, that a rose is beauti- 
ful, is red, is fragrant, thus affirming that the one 
cause, the rose, produces several distinct effects upon 



INDUCTION 145 

me; but we know that what we call " the rose" is 
a number of causes, that its form, its reflection of 
light, its emission of particles which go into the 
nasal passages, etc., all are different causes having 
different effects. 

The same is true of effects that we can not dis- 
tinguish as unlike, and therefore speak of as if 
really like and yet due to unlike causes; and here 
again we so speak even of effects that we may be 
able to distinguish by analysis. For example, we 
say indigestion is due to kind of food, eyestrain, 
nerve fatigue, grief, etc. ; so also of headache, death, 
motion. Closer analysis would show that when in- 
digestion, for instance, occurs following different 
irritants, other effects due to their difference, are 
also present, while the cause of the indigestion alone, 
if ascertained, will be found to be the same. So 
in every case where apparently like effects follow 
unlike causes. 

There is then no defect in the laws of uniformity, 
no exception to them, apparent exceptions being due 
to our imperfect observation. 



CHAPTER IX 

THE CAUSAL BASIS FOR INDUCTION 

33. Induction Based on Assumed Causal Con- 
nection. — It is evident that induction itself is 
extremely simple, and needs few rules, and no 
elaborate explanation. It is an immediate infer- 
ence fully warranted by the laws of causation and 
uniformity. But, to have scientific value, to at- 
tain real truth, it must be an inference from " an 
observed causal connection," as stated at the close 
of the first paragraph of Section 30. The estab- 
lishment of causal connection, the basis for scien- 
tific induction, is therefore of great importance, 
for it is only because of this causal fact that we are 
authorized to make the inductive " leap " from 
some to all. Deferring consideration of the ways 
of proving causal connection to the next section, let 
us here examine two familiar uses of induction, 
which do not rest on this scientific basis. 

33 a. Enumeration of Cases. — It is a familiar 
and accepted fact of mind that when experiences 
have occurred together, and one recurs, the others 
tend to recur with it ; and because this suggestion 
of mental states by others originally associated 

146 



CAUSAL BASIS FOR INDUCTION 147 

with them, is so common and familiar, not only do 
we usually expect this connection in memory, but 
in the external world. When outside facts, things, 
forces, impress themselves strongly and frequently 
upon our minds, and when later one of these as- 
sociated impressions recurs, we expect the others 
to recur with it, not merely in memory, but as 
actual new impressions due to renewed action of the 
external cause upon us. 

The more frequently, therefore, we receive im- 
pressions 1 together, the more confidently will we 
expect the recurrence of one to be attended by the 
others. The basis of this expectation is, however, 
as indicated above, not a scientifically established 
causal connection, but merely psychological, a 
transfer of the psychological law of suggestion 
from the inner mental sphere, where it does 
operate, to the outer material sphere, where it holds 
no sway. The fact, however, that cause and effect 
are always found together, justifies at least a sup- 
position that two concurrent impressions may rep- 
resent a causal connection, though not the belief 
that they certainly do. This method of multiply- 
ing cases of concurrent phenomena, therefore, is 
valuable in suggesting causal connections among 
circumstances constantly present, and in furnishing 
occasions for testing such connections by the 
methods of Section 34. It is valuable, also, for 
the many cases in everyday life, where scientific 



148 ESSENTIALS OF LOGIC 

analysis is impracticable, or not warranted because 
of the trivial nature of the circumstances to be 
explained. 

Very many of our proverbial sayings, supersti- 
tions, and popular rules are inductions based on 
mere count of cases. They are often incorrect, the 
cases being too few in number to indicate even 
plausible connection, or the exceptions when only 
one of the supposedly connected circumstances oc- 
curs, being passed over without notice; e. g., all 
crows are black, all malaria yields to quinine, all 
men have their price. 

33 b. Analogy. — The enumeration may be of 
concurrent qualities in two cases, instead of pairs 
of qualities, or marks, in many cases. The two 
methods are often equally available. From simi- 
larity of elevation, latitude, proximity to the sea 
and to the mountains, we might infer by the method 
of analogy that one place would have a season like 
the other. From likeness in appearance, odor, 
juiciness, consistency of two fruits, we might by 
analogy infer likeness in another quality, taste. 
Yet the two might be plum and persimmon. Mere 
analogy is never proof. It often suggests lines of 
investigation leading to proof. 

Enumeration and analogy may be described re- 
spectively as follows : if many cases have two com- 
mon characteristics, then other cases having one of 
these two, will probably have the other also; and, 



CAUSAL BASIS FOR INDUCTION 149 

secondly, if two cases have many common charac- 
teristics then other characteristics in the one will 
probably be found in the other. As the " other " 
characteristics in the inference may be any other, it 
is equivalent to all others. This, taken strictly, 
would mean absolute identity, so the expression can 
not be strictly construed, but is to be considered as 
merely suggestive. 

It is evident that these two modes of induction 
have no warrant except in the assumption that there 
is causal connection between the concurring cir- 
cumstances or characteristics. This connection be- 
ing assumed, and not proven, the induction is there- 
fore very hazardous, and should be so held, until 
by some scientific method the assumed causal con- 
nection is shown to be real. 

33 c. Probability. — Such inductions as result 
from enumeration or analogy are, then, not certain, 
but only more or less probable. This probability 
reaches a high degree in cases of phenomena con- 
curring frequently and without exception through 
a long period. That day and night will continue 
to follow each other is highly probable, though not 
certain; so also are changes in the tides, prevailing 
winds, average weather for different seasons, ra- 
cial characteristics, revolutions under oppression. 

The mathematical doctrine of probability is of 
service here. By it the " chance," or probability of 
concurrence of phenomena, without causal connec- 



150 ESSENTIALS OF LOGIC 

tion, may be estimated; then, if two phenomena oc- 
cur together either more or less often than chance 
would explain, they are probably causally connected. 
If, for example, one bag contains five balls, three 
of them white, the probability of drawing a white 
ball is 3-5 ; if another bag contains seven balls, four 
of them white, the probability of drawing a white 
ball from it is 4-7. The probability of drawing two 
white balls in succession, one from each bag, is 

3-5 x 4-7, or I2 "35- 

If, again, in a certain place, the average fre- 
quency of rainy days for many years has been one 
in three, while the average frequency of east winds 
has been one in four, then the probability of rain 
and east wind coming on the same day, without 
causal connection, is 1-3 x 1-4, or 1-12. If, then, 
rain and east wind concur on the average more than 
one day in twelve, the probability is they are 
causally connected; if less than one day in twelve, 
that there is counteraction; if just about one in 
twelve, that there is no causal bond. 

In this way we can set aside phenomena probably 
not causally affecting our investigation, thus nar- 
rowing the field of observation of possible causes 
and effects. 

When a real exception occurs, the claim of reality 
having been very carefully scrutinized, then we 
must give up our universal, and be content with 
" many " or " most " or " nearly all." 



CAUSAL BASIS FOR INDUCTION 151 

Statistics covering a great number and variety of 
cases, as the census, mortality tables, etc., are valu- 
able instances of enumerative probability, form- 
ing bases for induction as to the future of popula- 
tion, crops, term of life, etc., thus giving us rules 
from which we deduce conclusions as to particular 
periods, or individuals, or groups. 

34. Methods of Proving and Estimating 
Causal Connection. — The words, " change," 
" event," " circumstance," " phenomenon " are 
used as practical equivalents. A " case," or " in- 
stance " is a group of circumstances, including the 
phenomenon under investigation, or associated with 
it in some way. 

Cause and effect always being found together, 
the presence of either necessitating the presence of 
the other, it follows: 

(1) If two instances agree in every circumstance 
but two, these two are cause and effect. 

(2) If instances agree in only two circumstances, 
these two are cause and effect. 

(3) If two circumstances always vary together, 
they are either cause and effect, or effects of a com- 
mon cause. 

(4) If some instances agree only in the presence 
of two circumstances, while others agree only in 
their absence, these two are cause and effect. 

These methods are discussed in the following 
sections. Their purpose is to solve the problem: 



152 ESSENTIALS OF LOGIC 

given a cause, to find its effect; or, given an effect, 
to find its cause. 

34 a. The Method of Difference.—" If two 
instances agree in every circumstance but two, 
these two are cause and effect." The use of this 
principle to prove causal connection is called the 
" method of difference," because the two instances 
differ only in the presence of the cause and the 
effect, being alike in every other particular except, 
of course, time and place. If, then, the phe- 
nomenon under investigation, frost, let us say, be 
present with a number of other circumstances such 
as clear sky, still air, temperature freezing, dew- 
point below freezing; while on another occasion, 
all the circumstances being the same as above, ex- 
cept that the temperature, for example, is above 
freezing everywhere, and there is no frost; then we 
conclude that frost and temperature are causally 
connected. So we might reach a similar conclu- 
sion if the second instance differed from the first 
only in the absence of frost and the presence of 
high wind, or in cloudy sky and no frost. 

Or, if a cause be given to find its effect, as for 
example the effect of benzoate of soda, as a food 
preservative, upon health, two men as much alike 
as possible in every way likely to influence the re- 
sult, might be kept under the same conditions of 
diet, exercise, and general hygiene, one being given 
food with the benzoate, the other the same food 



CAUSAL BASIS FOR INDUCTION 153 

without the benzoate. Should the former show 
signs of injury to health, and the other not, the 
conclusion would be that benzoate of soda is the 
cause. 

A room in a locality where there was much 
yellow fever was divided by a partition of fine 
wire screen. On one side the bedding and clothes 
of yellow fever patients who had died, soiled with 
the foul evidences of the dread disease, were used. 
On the other side of the screen partition everything 
was fresh and clean, but some mosquitoes which 
had bitten yellow fever patients, were introduced. 
Cases of fever developed on the clean side, where 
the mosquitoes were; none on the foul side where 
no mosquitoes were. The presence on one side 
of the mosquitoes and the fever, and the absence 
on the other side of only these two circumstances, 
give an almost ideal instance of the method. The 
addition of the foul bedding on the side where no 
fever developed, could not prevent the fever, so 
that the cogency of the method is not affected; and 
as no fever followed the use of the contaminated 
bedding, the presumption is that it is not a cause 
of the fever. 

When Stanley observed in Africa that those of 
his party who slept under netting to avoid the an- 
noyance of the mosquitoes, did not have malaria, 
while others not so protected did, he concluded 
rightly by the method of difference that the netting 



154 ESSENTIALS OF LOGIC 

had something to do with the freedom from ma- 
laria. He supposed, however, that the netting 
strained the " miasma " out of the air; we now 
know it kept the malaria-charged mosquitoes from 
introducing the germs of the disease by their bite. 

34 b. The Method of Agreement. — " If in- 
stances agree in only two' circumstances, these two 
are cause and effect." This principle gives us the 
" method of agreement." If the phenomenon un- 
der investigation, as, for example, indigestion, oc- 
curs after dinner for a number of days, some warm, 
some mild, some cool, the dinner being varied more 
or less every day, and it is found that the only arti- 
cle of food eaten every day was cabbage, that 
would be indicated as the cause of the indigestion. 
It would then be in order to apply the method of 
difference, not eat the cabbage, and the indigestion 
not recurring, we should have proof. 

But why should we not be content with the evi- 
dence of the method of agreement alone? Not be- 
cause of any defect in theory, but because in prac- 
tice we can not be sure of having observed all the 
circumstances that are present and may cause the 
phenomenon. In the example above, there might 
be appendicitis, only now become acute, or nerv- 
ous disorder, or some other circumstance not easily 
observable; and if the indigestion persists after the 
cabbage is eliminated, the case must be examined 
more closely for other circumstances. 



CAUSAL BASIS FOR INDUCTION 155 

The method, therefore, while valuable for its sug- 
gestiveness, and often affording practical certainty, 
yet because we can not always eliminate all but two 
circumstances in a series of cases, or because we 
can not always distinguish effects that are actually 
unlike and therefore due to unlike causes, because, 
in short, our powers of arrangement, observation, 
and analysis are not always adequate, is often un- 
certain in its results. 

The greater the number of instances of agree- 
ment, the greater is the probability of causal con- 
nection, for in a series of many cases the likeli- 
hood that an exception will occur is greater, if the 
two circumstances which have many times con- 
curred are not really cause and effect. If all but 
a few circumstances have been eliminated in the 
series of instances examined, experimenting with 
these in turn may show which is the cause of the 
effect investigated. 

The method goes further than simple enumera- 
tion, for it calls for the ultimate exclusion of all 
but two circumstances, the cause and effect, in the 
course of the series of cases observed; while 
enumeration takes note merely of the fact that two 
circumstances occur together, disregarding the 
equally significant fact of the presence of others 
which might be connected with these two by a 
causal bond. 

The method is useful in the many cases where 



156 ESSENTIALS OF LOGIC 

it is not possible to eliminate the two circumstances, 
as required by the method of difference, and as has 
been shown above may finally suggest a way of us- 
ing that more conclusive method, which is always 
to be desired. 

34 c. The Method of Variations. — This is not 
a different method of establishing causality, but an 
application of either of the preceding methods to 
the change in quantity, degree, or intensity of cir- 
cumstances, instead of the change in presence or 
absence of the circumstance as a whole. 

"If two circumstances always vary together, 
they are either cause and effect, or effects of a com- 
mon cause." It often happens that we can in a 
series of cases eliminate neither the two circum- 
stances which are causally connected, so> as to ap- 
ply the method of difference, nor yet all other cir- 
cumstances but these two so as to use the method of 
agreement. In many such cases it happens that the 
circumstances vary in intensity, or degree; and so, 
substituting for the circumstance as a whole, its 
quantity, or degree, substituting for its presence, 
the amount of its energy, we take this amount for 
a new circumstance, and proceed by the methods of 
agreement or difference. 

If two circumstances appear in one instance, and 
in a second also these two appear, each with a dif- 
ferent intensity from that of the first instance, no 
others being changed, then the method of differ- 



CAUSAL BASIS FOR INDUCTION 157 

ence warrants the conclusion of causal connection 
between the two. 

Or if, while several quantities vary in some of a 
number of instances, yet only two vary in all of 
these instances, the method of agreement points to 
causal connection between these two varying quan- 
tities. 

The method is usually and more conveniently 
treated as a distinct method, and is called " the 
method of variations." 

When two bodies are rubbed together, and the 
force exerted is exactly measured, it is found that 
the heat generated by the friction is exactly in pro- 
portion to the force used in rubbing, whence 
causal connection is inferred. 

The tides vary as the position of the moon rela- 
tive to the earth changes ; the mercury rises or falls 
in the thermometer as the heat of the atmosphere 
increases or diminishes; if crime be shown to in- 
crease or diminish with poverty, causality may be 
argued; so if earning power increases with school 
period. 

The method of variations is also of great value 
in determining quantitative relations, the mathe- 
matical laws of causes already discovered by other 
methods. In this way the ratio of causal energy 
to the energy of the effect is estimated. Care must 
be taken that there is not some new cause operating 
beyond the limits observed. It takes a certain 



158 ESSENTIALS OF LOGIC 

amount of fuel to increase the speed of a steamer 
one mile per hour, but the additional amount dif- 
fers according to the amount already attained. It 
takes more to fatten pork from 200 to 300 pounds, 
than from 100 to 200. Water contracts with loss 
of heat as a rule, but expands from 39 to 32 de- 
grees. 

34 d. The Joint Method of Agreement and 
Difference. — " If some instances agree only in the 
presence of two circumstances, while others agree 
only in their absence, these two are cause and effect." 
The first clause of this canon is evidently the method 
of agreement exactly, and causal connection is 
thereby indicated. For the " others " to add force 
to the series of instances of this first clause, the 
circumstances in these " others " should be as much 
like those in the former series as possible. Were 
the circumstances in any one instance of the latter 
series exactly like those in any one of the former 
series, except for the absence of two that were in 
the former case, the conditions of the method of 
difference would be fulfilled, and further instances 
would be unnecessary. Hence the name of the 
method above. 

But the supposition is that the requirements of 
the method of difference are not fulfilled, that there 
are only many points of similarity between the sec- 
ond series of instances and the first, and that while 
any two or more of these latter cases may agree in 



CAUSAL BASIS FOR INDUCTION 159 

several ways, yet there is nothing common to all of 
them save the absence of the two circumstances con- 
curring throughout the former series; that is, the 
second set agree in the absence of the two. The 
method is therefore called by some, the method of 
double agreement. 

The places in which the famous Albemarle pip- 
pin reaches its highest excellence of beauty, fla- 
vor, and soundness, agree in elevation, soil, and 
climate. The same apple has been grown in many 
other places like the former in many ways, yet not 
all agreeing in any one particular except in differ- 
ing considerably from the former places in eleva- 
tion, soil, or climate ; in these latter places the super- 
ior excellence of the fruit is notably absent. 

In case of merely frequent, not invariable, pres- 
ence or absence together of two circumstances, 
there may be causal connection, some unobserved 
third circumstance being part of the cause or the 
effect, or operating to counteract the cause; be- 
cause of its omission, if part of the whole cause, 
the effect will not appear, even though the other 
causal circumstance be present ; because of its pres- 
ence, if counteractive, the cause will not produce 
the effect. Sir John Herschel, for example, is said 
to have thought that the full moon tends to clear 
the sky of clouds, because of the warmth radiated 
from its surface. If this be true, the reason some 
nights of full moon are not clear would be found 



160 ESSENTIALS OF LOGIC 

in the presence of some counteracting cause, or 
in the absence of some circumstance equally neces- 
sary to the production of the effect. 

35. Combination of Causes. — It often hap- 
pens that after certain parts of a complex effect 
have been assigned to their causes, a yet unexplained 
part remains. It is evident that this must be due 
to some other cause than those already ascertained 
and a more careful investigation may discover the 
hitherto unobserved element. This is commonly 
called the " method of residues," and proceeds ac- 
cording to the following obvious rule: Setting 
aside the known causes and their effects, any re- 
maining circumstances of a complex case must in- 
clude all other causes and effects in the case. This 
is so evident that the principle hardly deserves the 
name of a method; yet its frequent and great use- 
fulness show its importance. 

A stock example is the discovery of Neptune, 
whose position at a stated time was calculated as the 
explanation of a certain unexplained perturbation 
in the movements of Uranus. 

The passage of an electric discharge through the 
air was observed to be attended by a peculiar odor, 
further investigation of which led to the discovery 
of ozone, a form of oxygen. 

In the second place, in case of causes producing 
effects of the same kind, such as the velocity of the 
same body acted upon by several forces, the effect 



CAUSAL BASIS FOR INDUCTION 161 

may often be calculated before it is observed. To 
state it succinctly: From the laws of several 
causes acting together, their joint effect, if of the 
same kind, may be calculated. Given the velocity 
of a stream and of a boat in still water, the speed 
up and down stream is easily estimated; a very 
simple example. Because, however, of balancing 
forces, the practical use of the principle is often 
much more difficult than might be expected from its 
simplicity. The process has been called " the de- 
ductive method," the term including the induction 
leading to the laws of the causes, the deduction from 
these to the joint effect, and the testing, or verifica- 
tion of this deduction by actual observation. 

36. Hypothesis. — When a phenomenon in- 
terests us for the first time, or in a new way, and 
we do not know its kind or its cause, we guess. 
An unusual sound in the house at night, a strange 
light in the sky, a curious pain, an unexpected cool- 
ness on the part of a friend, any circumstance not un- 
derstood, and sufficient to arouse interest, is fol- 
lowed by an immediate effort of the imagination to 
explain it by assigning it to its class or its cause. 
The sound in the house is only a rat, the light must 
have been a meteor, the pain was a twinge of neu- 
ralgia, the coolness of the friend must have been 
because of a false report. 

This tendency is natural, universal, and in 
trivial affairs, spontaneous. But it may also be de- 



i62 ESSENTIALS OF LOGIC 

liberate, guided by intelligent volition, and of great 
scientific value. In things we deem unimportant, 
we are satisfied with a guess. In less trivial cases, 
we investigate, test, and seek to prove. The scien- 
tific use of the imagination in this connection, is to 
make suppositions regarding causation. A cause 
or its law may be assumed, or both ; or an effect or 
its law; but the supposition that a certain cause 
will be followed by such and such an effect has no 
scientific significance, for the mere use of a cause 
to learn what effect it would produce, gives us the 
knowledge without the need of previous supposi- 
tion. If, however, we are investigating a certain 
effect, we must suppose some definite cause or other 
may produce it, or we can not make any progress 
toward learning the cause, unless it happen to fall 
under our observation. The use of a cause to see 
whether it will produce a certain effect implies that 
we have made the supposition that it may; for if 
we are sure it will not, we will not try it. A scien- 
tific hypothesis, therefore, assumes a cause for a 
given effect, or a law for a given cause, or a law for 
a given effect. 

Lying in the mind close to the bed-rock princi- 
ple that every event has a cause, is the tendency to 
ask and seek answer to the question, what is the 
cause of this event which interests me? In observ- 
ing a mere series of cases as in enumeration in 
Section 33 a, we reject some circumstances, on the 



CAUSAL BASIS FOR INDUCTION 163 

hypothesis that they are no part of the cause of the 
event we seek to explain; and we select others on 
the hypothesis that they are the cause. In analogy, 
as described in Section 33 b, we suppose some cause 
explains the similarity of qualities in the two cases. 
Especially when we experiment, as for example, in 
the method of difference, do we make hypothesis 
that the omission of a certain circumstance will 
be attended by the disappearance of the phe- 
nomenon ; and we omit this circumstance. In fact, 
we can make no progress without the aid of this 
faculty, imagination, in framing hypotheses. 

Despite the legal maxim that the accused is sup- 
posed to be innocent until proven guilty, no trial 
can proceed in seriousness unless the guilt of the 
accused be supposed at least possible ; this much it is 
the function of the grand jury to decide, and this 
is the logical significance of the indictment, that 
the hypothesis of guilt is possible. 

Many hypotheses were made and cast aside be- 
fore astronomy became heliocentric. Many and 
varied speculations as to the structure of matter 
preceded the atomic hypothesis, so long and so 
usefully held, but even now apparently yielding to 
the pressure of advancing knowledge. If we count 
dead hypotheses, the science of medicine has buried 
more than double as many as even a comic paper 
would insinuate. 

The multitude of these discarded relics of prog- 



1 64 ESSENTIALS OF LOGIC 

ress suggests the question, asked sometimes in 
scorn, yet a rightful question: of what value are 
hypotheses, if so many have proven untrue? The 
answer has already been suggested above. Hy- 
potheses are the stepping-stones of science, and 
if now and then one is overturned, or proves too 
slippery for foothold, or is merely left behind for 
another in advance, surely here is found argument 
against neither stepping-stone nor hypothesis. 
How, then, may true hypotheses be known from 
false? The answer to this question will be found 
in the next two sections. 

37. Verification. — The test known as " veri- 
fication " is so often thought to establish the truth 
of an hypothesis, that it should be said at the out- 
set that verification is never proof of the truth 
of a general hypothesis, but is often proof of its 
falsity; or it merely leaves the possibility of truth 
untouched or even strengthened by the fact that a 
test which might have proven falsity, did not. The 
value of the process is therefore purely negative, 
as will appear in the following discussion. 

When, as in Section 35, from the known inductive 
laws of certain causes, we deduce their joint effect, 
and then by observation with or without experiment 
we test our deductive conclusion by comparison with 
the actual case, the process, often called "the de- 
ductive method, " either " verifies " the conclusion 
or proves it false. The important point is that 



CAUSAL BASIS FOR INDUCTION 165 

it is the deductive conclusion, the particular fact, 
that is verified or not, and not the inductive prem- 
ise, the general proposition. We know from the 
laws of the syllogism that if the conclusion be false, 
a premise is false; while if the conclusion be true, 
nothing follows as to the truth of the premises. 

So in the use of hypotheses, when we seek to 
find, not as above, the effect, but the cause of a 
phenomenon, the steps in the procedure are the 
same, the nature of the " verification " the same, 
and the bearing upon truth or falsity the same. 
The difference is that instead of having for prem- 
ise the known inductive laws of causes, we make 
hypothesis of a cause or its law, deduce from that 
our conclusion, and test it by observation with or 
without experiment as in the other case. 

The significance of the result is the same. If 
the observed facts agree with the deductive con- 
clusion, that conclusion is " verified," but we know 
that the truth of the premise, our hypothesis, does 
not follow. So the verification is of the single 
fact, not of the hypothesis. However, repeated 
deductions from an hypothesis, verified without ex- 
ception by observation, have a strong tendency to 
foster belief in its truth ; and we must guard against 
the acceptance of this negative confirmation as 
proof; it is merely lack of evidence of falsity; it 
affords presumption of truth, not proof. 

On the other hand, if a conclusion correctly de- 



1 66 ESSENTIALS OF LOGIC 

duced from an hypothesis, is by observation found 
contrary to the fact, the hypothesis must be given 
up; for the falsity of a conclusion does involve the 
falsity of the premise. 

The Ptolemaic hypothesis that the earth is the 
center around which sun, moon, and planets revolve, 
was discarded because the consequences deduced 
from it were not in accord with the facts. 

The deduction that, on the hypothesis of the 
identity of lightning and terrestrial electricity, a 
spark could be gotten from a kite-string, was veri- 
fied by Franklin's experiment. 

The hypothesis that sound is conveyed by vibra- 
tory motion of the air has led to many deductions 
verified by observation, one of the most striking 
being the photographic shadow caused by the con- 
densation of air particles in front of the advancing 
sound wave. 

The old hypothesis that nature abhors a vacuum, 
offered to explain the rise of water in a pump, was 
overthrown by the fact that the water would not 
rise beyond a definite height. 

Verifications, then, may overthrow an hypothesis, 
or they may either establish or overthrow a deduc- 
tion from an hypothesis. They are not proof, yet 
many accept them as proof. What, then, is proof? 

38. Proof. — As intimated in Section 34 b, 
strict proof of causal relation is found only by the 



CAUSAL BASIS FOR INDUCTION 167 

method of difference. However strong may be the 
presumption of truth, however great our confidence 
that we have found the truth, yet there is no strict 
logical proof of causal relation short of exact ful- 
fillment of the rigid requirements of the method of 
difference. So must it be in the case of an hy- 
pothesis, just as in any other case of causation. 
First, the hypothesis must be shown to explain all 
the facts ; that is, the cause we assume must be found 
producing all the effects of the kind, deduced from 
the hypothesis and tested by verification ; which cor- 
responds to the first set of circumstances of the 
method of difference. Secondly, it must be shown 
that no other hypothesis can explain the facts; that 
when the assumed cause is absent, the effects will 
not be found; or that other hypotheses lead to con- 
clusions contrary to facts. 

In the example of Section 34 a, for instance, the 
hypothesis was made that a mosquito which had 
bitten a yellow fever patient might convey the dis- 
ease. The experiment showed the hypothesis ex- 
plained the fact, and the freedom from fever on 
the other side of the screen, where a rival hypothe- 
sis, the contagion of foul bedding, was tried, proved 
that no other plausible hypothesis would explain 
the conveyance of the fever. This was proof, and 
therefore the surgeon-general of the United States 
Army gave orders that the only special precaution 



1 68 ESSENTIALS OF LOGIC 

to be taken in cases of yellow fever thereafter 
should be the screening of patients so that mos- 
quitoes could not bite them. 

When the circumstances of a crime are such that 
they can be explained only by the guilt of a certain 
person, he is properly convicted on " circumstantial " 
evidence. The prosecution will try to prove that 
no other hypothesis will explain the crime; the de- 
fense that some other will. If the defense fail to 
establish some other tenable hypothesis, or of course, 
some irreconcilable fact such as an alibi, the hy- 
pothesis of guilt prevails, and rightly. 

The radical change in the lives of many after 
profession of Christian faith can be explained only 
on the hypothesis of a radical change in their na- 
ture, and such cases afford logical proof of the 
vital power of Christianity. 



CHAPTER X 

RESULTS OF INDUCTION 

39. Discovery. — Any true induction may lead 
to the discovery of new facts; for the sweep of the 
inductive universal includes unobserved cases of the 
operation of the cause in question; and we may use 
the induction as a major premise from which to 
draw a deductive conclusion of some less general 
truth or some particular fact. Thus we are able to 
predict that observation will confirm our conclusion ; 
that a fact hitherto unknown will be found true. 
This is evidently like the process described in Sec- 
tion 35 under the head of " combination of causes," 
and also that used in verifying hypotheses in Sec- 
tion 37. All these are only instances of deduction 
from general premises. 

In this way the astronomer predicts eclipses, the 
return of a comet, the position of a new planet ; the 
chemist from his inductive law of progressive qual- 
ities predicts new elements; the economist from in- 
ductions regarding demand and supply predicts 
changes in the market, panics, prosperity ; the geolo- 
gist foretells future conditions of river-beds, moun- 
tains, plains, valleys, and coasts. 

169 



170 ESSENTIALS OF LOGIC 

40. Law. — A law is the statement of a uni- 
formity. The sources of knowledge being two, as 
in Section 29, laws are of two kinds : intuitive, dis- 
cerned by the intellect; inductive, based on observa- 
tion by the senses. Intuitively discerned law, such 
as the axioms of mathematics and of logic, being 
known originally in the form of universal proposi- 
tions, are thus the source of many subordinate laws 
derived from them by deduction. Hence they are 
called " primary laws." Inductively attained law, 
such as the laws of sound and of heat, being based 
originally on particular facts, may thus be explained 
by higher and wider laws, until final explanation is 
attained in universal laws beyond which the human 
mind can not reach. These wide inductive uni- 
versal, because they stand last in the order of at- 
tainment are called " ultimate " laws. Though we 
may be sure there are ultimate laws, we may not be 
sure whether laws we have reached are those of 
widest scope, whether they may not be included in 
some other still wider. It would seem hardly pos- 
sible to go further than Newton's Laws of Motion. 
The Law of Gravitation is another notable example 
of law that so far as we know, is ultimate. 

41. Natural Law. — Inductive laws depend 
upon and are formed in accordance with intuitive 
principles; all concrete knowledge is cast in these 
abstract forms. Even the axioms of pure mathe- 
matics may be applied to definite numbers of con- 



RESULTS OF INDUCTION 171 

crete things ; the laws of pure logic are useful only 
when operative in actual thoughts ; the formal prin- 
ciples of ethics do not guide conduct unless effec- 
tive in the real act; the intuitive laws of causation 
are of practical value only when connected with 
particular causes. 

Thus, the axioms of uniformity of Section 32 
are intuitive, pure, formal, without content; but 
when applied to the actual causes and effects of na- 
ture, the resulting uniformities of concrete cases of 
causation are natural laws. Natural law is expres- 
sive of the uniformities in the sphere of causation, 
and is logically opposite to moral law, which is ex- 
pressive of the uniformities in the sphere of free- 
dom; natural law declares what is in nature, moral 
law commands what ought to be in conduct. Moral 
law is obeyed or violated; natural law is neither 
obeyed nor violated. When a rock is thrown up- 
ward from the earth, the law of gravitation is not 
violated, but a new cause, the energy of the mus- 
cles, is put into operation according to its own law. 

A miracle is not a violation of law. The Maker 
of the Universe may use either a natural cause or 
law unknown to us to work what we call a miracle, 
or He may employ His creative power, itself the 
cause of all causes. 

The question of the possibility of resolving all 
natural law into a single ultimate law, has been 
much discussed. Whether or not we shall ever 



172 ESSENTIALS OF LOGIC 

bridge the chasm between present multiplicity and 
such a unity, may be doubted, but that there is such 
unity we may be sure ; for, " In the beginning God 
created the heavens and the earth." 

42. Science. — The intuitive principles of 
space and time, developed by deduction, give us the 
pure science of mathematics; those of thought and 
causation give logic, which is the pure framework 
of every science. Sciences of facts and causes, de- 
veloped according to the intuitive principles con- 
trolling induction, but systematizing experiences, 
give us such empirical sciences as physics and chem- 
istry. Sciences which have intuitive knowledge 
alone as their object-matter, are pure sciences; those 
which deal with sensuous knowledge, according to 
intuitive principles, to be sure, are empirical sci- 
ences. 

Pure sciences are necessarily deductive, for they 
descend from the universal, directly known truths 
of intellect. Empirical sciences are at first induc- 
tive, and continue largely so, for they ascend from 
individual facts to general laws; yet no sooner is 
the first general law attained than the way is thereby 
opened for deductions from it to new subordinate 
laws or facts. As knowledge progresses, there- 
fore, an inductive science becomes more and more 
deductive. Theoretically, when all the laws of an 
empirical science have been discovered, the science 
would cease to be inductive, and be deductive only; 



RESULTS OF INDUCTION 173 

but this theoretical case has not occurred, nor are 
we likely to reach it. Astronomy, however, for in- 
stance, has been developed largely by deductions 
from the laws of gravitation and motion. There 
are, therefore, no sciences that are always wholly 
inductive. 

The systematic arrangement in their proper re- 
lation of all things knowable — principles, causes, 
laws, and classes, is the goal of science. 



INDEX 



Reference to Pages 



Abstraction, 15 
Affirmation, law of, 47 
Agreement and Difference, joint 

method of, 158 
Agreement, method of, 154 
Ambiguity, 123 
Analogy, 148 

Begging the question, 125 

Causal basis for induction, 146 
Causal basis assumed, 146 
Causal basis proved, 151 
Causation, 142 
Cause, nature of, 143 
Causes, combination of, 160 
Chance, 149 
Change, axiom of, 142 
Classification, 28 
Co-extension, 28 
Combination, inference by, 77 
Combination of causes, 160 
Compound propositions, 54 
Conception, 16 
Concepts, 17 

Conditional propositions, 105 
Conditional syllogisms, 115 
Contradictories, 46 
Contraposition, 83 
Contraries, 47 
Contraversion, 83 
Conversion, inference by, 79 
Co-ordination, 27 



Deduction, 75 
Deduction, immediate, 76 
Deduction, mediate, 86 
Deductive method, 164 
Definition, 38 
Definition, rules of, 40 
Denial, law of, 48 
Dichotomy, 34 
Difference, method of, ij 
Discovery, 169 
Disjunctive propositions, 
Division, 32 
Division, rules of, 34 



107 



Enthymemes, 90 
Enumeration, 146 
Epicheirema, 92 
Episyllogism, 92 
Exclusion, law of, 48 
Extension and intension, 
of, 17 

Fallacy, 122 

Figure and mood, 118 

Forms of thought, 14 

Generalization, 16 
Genus, 30 

Hypothesis, 161 

Hypothetical propositions, 105 

Illicit process, 88 
Immediate inference, 77 



law 



175 



176 



INDEX 



Implied judgments, 76 
Induction, results of, 169 
Inductive inference, 139 
Inference, kinds of, 75 
Inference, nature of, 75 
Intension and extension, 18 
Intersection of notions, 27 
Inversion, 83 

Joint method of agreement and 

difference, 158 
Judgments, 52 

Law, nature and kinds of, 170 

Limitation, conversion by, 80 

Logic a distinct science, 12 

Logic defined, 1 

Logic not an art, 11 

Logic related to all science, 13 

Major, minor, and middle terms, 

87 
Marks, kinds of, 24 
Marks, nature of, 15 
Mathematical propositions, 58 
Mathematical syllogisms, 117 
Misproof, 124 
Moral law, 171 

Natural law, 170 
Notions, kinds of, 19 
Notions, nature of, 15 
Notions, relations of, 26 

Obversion, 79 

Polytomy, 34 
Premises, 86 
Probability, 149 
Proof, 166 
Proper names, 21 
Propositions, 52 
Propositions, conditional, 105 
Propositions, disjunctive, 107 



Propositions, 
Propositions, 
Propositions, 
Propositions, 
Propositions, 
Propositions, 
Propositions, 
Propositions, 
Propositions, 
Prosyllogism, 



hypothetical, 105 
individual, 58 
kinds of, 54 
methematical, 58 
quality of, 55 
quantity of, 56 
relations of, 81 
strict form of, 83 
symbols of, 58 
92 



Quality of propositions, 55 
Quantity of propositions, 56 
Quantity, words showing, 57 

Residues, method of, 160 
Rules of definition, 40 
Rules of division, 34 
Rules of syllogism, 87 

Science, 172 

Scientific induction, 140 

Sorites, 92 

Species, 30 

Subordination, 27 

Syllogism, conditional, 115 

Syllogism, incomplete, 90 

Syllogism, mathematical, 117 

Syllogism, nature and parts of, 

Syllogism, rules of, 87 

Symbols of propositions, 58 

Term, meaning of, 18 
Terms of syllogism, 87 
Thought, nature of, 75 
Thought, primary laws of, 46 
Trichotomy, 34 

Undistributed middle, 88 
Uniformity, 144 

Variation, method of, 156 
Verification, 164 



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